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  • CR: 5.14
  • Optimization
  • geostatistics
  • Springer  (46)
  • American Chemical Society
  • American Institute of Physics
  • Annual Reviews
  • Elsevier
  • Periodicals Archive Online (PAO)
  • Wiley
  • 2005-2009
  • 1990-1994
  • 1980-1984  (46)
  • 2008
  • 2007
  • 1982  (28)
  • 1980  (18)
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  • Springer  (46)
  • American Chemical Society
  • American Institute of Physics
  • Annual Reviews
  • Elsevier
    • +
Years
  • 2005-2009
  • 1990-1994
  • 1980-1984  (46)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Conjugate direction methods with variable storage (1982)
    Springer
    Mathematical programming 23 (1982), S. 326-340 
    Details
    ISSN: 1436-4646
    Keywords: Optimization ; Quasi-Newton ; Conjugate Gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we study conjugate gradient algorithms for large optimization problems. These methods accelerate (or precondition) the conjugate gradient method by means of quasi-Newton matrices, and are designed to utilize a variable amount of storage, depending on how much information is retained in the quasi-Newton matrices. We are concerned with the behaviour of such methods on the underlying quadratic model, and in particular, with finite termination properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583797
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  • 2
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    A smoothing-out technique for min—max optimization (1980)
    Springer
    Mathematical programming 19 (1980), S. 61-77 
    Details
    ISSN: 1436-4646
    Keywords: Optimization ; Nonlinear Programming ; Unconstrained Optimization ; Nondifferentiable Optimization ; Min—Max Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR n . Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581628
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  • 3
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    Fast Givens rotations for orthogonal similarity transformations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 47-56 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F30 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Fast Givens rotations with half as many multiplications are proposed for orthogonal similarity transformations and a matrix notation is introduced to describe them more easily. Applications are proposed and numerical results are examined for the Jacobi method, the reduction to Hessenberg form and the QR-algorithm for Hessenberg matrices. It can be seen that in general fast Givens rotations are competitive with Householder reflexions and offer distinct advantages for sparse matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459074
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  • 4
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    Exact solution of linear equations usingP-adic expansions (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 137-141 
    Details
    ISSN: 0945-3245
    Keywords: (MR 1980) AMS(MOS) ; 65F05, 15A06, 10M10, 10A30 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector $$\bar x$$ such that $$A\bar x \equiv b$$ (modp m ) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation $$\bar x$$ . For matricesA andb with entries of bounded size and dimensionsn×n andn×1, this method can be implemented in timeO(n 3(logn)2) which is better than methods previously used.
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    URL: http://dx.doi.org/10.1007/BF01459082
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  • 5
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    Error bounds for computed eigenvalues and eigenvectors. II (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 201-206 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F05, 65F15, 65H10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, motivated by Symm-Wilkinson's paper [5], we describe a method which finds the rigorous error bounds for a computed eigenvalue λ(0) and a computed eigenvectorx (0) of any matrix A. The assumption in a previous paper [6] that λ(0),x (0) andA are real is not necessary in this paper. In connection with this method, Symm-Wilkinson's procedure is discussed, too.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400539
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  • 6
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    Reguläre Zerlegungen und Berechnung des Spektralradius nichtnegativer Matrizen (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 201-216 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary On the basis of a Rayleigh Quotient Iteration method in [10] and a Maximal Quotient Iteration method in [5, 8] two algorithms for solving special eigenvalue problems are developed. The characteristic properties of these methods lie in the application of iterative linear methods to solving systems of linear equations. The convergence properties are investigated. We apply the algorithms to the computation of the spectralradius of a nonnegative irreducible matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396060
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  • 7
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    Realistic error bounds for a simple eigenvalue and its associated eigenvector (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 113-126 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An algorithm is described which, given an approximate simple eigenvalue and a corresponding approximate eigenvector, provides rigorous error bounds for improved versions of them. No information is required on the rest of the eigenvalues, which may indeed correspond to non-linear elementary divisors. A second algorithm is described which gives more accurate improved versions than the first but provides only error estimates rather than rigorous bounds. Both algorithms extend immediately to the generalized eigenvalue problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396310
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  • 8
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    Characterizations of dominant and dominated solutions of linear recursions (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 421-442 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65Q05, 65F99, 39A10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Dominated solutions of a linear recursion (i.e. solutions which are outgrown by other ones) cannot be computed in a stable way by forward recursion. We analyze this dominance phenomenon more closely and give practically significant characterizations for dominated and dominant solutions. For a dominated solution, in particular, this leads to a stable computational method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399009
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  • 9
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    Stability of fast algorithms for matrix multiplication (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 63-72 
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    ISSN: 0945-3245
    Keywords: AMS (MOS): 15A63 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Non commutative fast algorithms to compute 2×2 matrix product are classified with regard to stability. An analysis of the rounding error propagation is presented for then×n matrix multiplication algorithms obtained by recursive partitioning.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395989
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  • 10
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    Least squares with a quadratic constraint (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 291-307 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F20 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present the theory of the linear least squares problem with a quadratic constraint. New theorems characterizing properties of the solutions are given. A numerical application is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396656
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  • 11
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    Matrices related to interpolatory quadratures (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 309-318 
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    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; 65D30 ; CR: 5.14 ; 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An explicit formula for the coefficients of interpolatory quadratures with knots of arbitrary multiplicity which uses the eigenvectors and principal vectors of certain matrices is derived. The construction and properties of such matrices are discussed, and applications for the evaluation of Gauss and generalized Gauss-Lobatto quadratures are indicated.
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    URL: http://dx.doi.org/10.1007/BF01396657
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  • 12
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    LU decompositions of generalized diagonally dominant matrices (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 57-69 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Using the simple vehicle ofM-matrices, the existence and stability ofLU decompositions of matricesA which can be scaled to diagonally dominant (possibly singular) matrices are investigated. Bounds on the growth factor for Gaussian elimination onA are derived. Motivation for this study is provided in part by applications to solving homogeneous systems of linear equationsAx=0, arising in Markov queuing networks, input-output models in economics and compartmental systems, whereA or −A is an irreducible, singularM-matrix. This paper extends earlier work by Funderlic and Plemmons and by Varga and Cai.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459075
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  • 13
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    Computing theCS decomposition of a partitioned orthonormal matrix (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 297-306 
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    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F25 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper describes an algorithm for simultaneously diagonalizing by orthogonal transformations the blocks of a partitioned matrix having orthonormal columns.
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    URL: http://dx.doi.org/10.1007/BF01396447
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  • 14
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    An algorithm for a linear diophantine equation and a problem of Frobenius (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 349-352 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 10B05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We solve the diophantine equation $$\sum\limits_{j = 1}^n {a_j x_j } = L$$ for nonnegative variablesx j , wherea j andL are positive integers. We characterize both the values ofL that lead to solutions and those that do not lead to solutions. We solve the Frobenius problem of finding the largest value ofL for which no solution exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403673
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  • 15
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    A generalization of the Stein-Rosenberg theorem to Banach spaces (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 403-409 
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    ISSN: 0945-3245
    Keywords: AMS(MOS):65F 10, 47B 55 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the first part of this note we prove a generalization of the Stein-Rosenberg theorem; the context is that of real Banach spaces with a normal reproducing cone and the operators involved are positive and completely continuous. Our generalization of the Stein-Rosenberg theorem improves the modern version of it as stated by F. Robert in [5, §2]. In the second part, we discuss briefly how our results are related to other versions of the Stein-Rosenberg theorem. In the last section we describe a situation to which the results in the first part can be applied.
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    URL: http://dx.doi.org/10.1007/BF01403677
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  • 16
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    On the sharpness of some upper bounds for the spectral radii of S.O.R. iteration matrices (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 69-79 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Sharpness is shown for three upper bounds for the spectral radii of point S.O.R. iteration matrices resulting from the splitting (i) of a nonsingularH-matrixA into the ‘usual’D−L−U, and (ii) of an hermitian positive definite matrixA intoD−L−U, whereD is hermitian positive definite andL=1/2(A−D+S) withS some skew-hermitian matrix. The first upper bound (which is related to the splitting in (i)) is due to Kahan [6], Apostolatos and Kulisch [1] and Kulisch [7], while the remaining upper bounds (which are related to the splitting in (ii)) are due to Varga [11]. The considerations regarding the first bound yield an answer to a question which, in essence, was recently posed by Professor Ridgway Scott: What is the largest interval in ω, ω≧0, for which the point S.O.R. iterative method is convergent for all strictly diagonally dominant matrices of arbitrary order? The answer is, precisely, the interval (0, 1].
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    URL: http://dx.doi.org/10.1007/BF01396371
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  • 17
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    The rate of convergence of an approximate matrix factorization semi-direct method (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 237-251 
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    ISSN: 0945-3245
    Keywords: CR: 5.14 ; 5.17 ; AMS(MOS): 65F10 ; 65N10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The definition of acceleration parameters for the convergence of a sparseLU factorization semi-direct method is shown to be based on lower and upper bounds of the extreme eigevalues of the iteration matrix. Optimum values of these parameters are established when the eigenvalues of the iteration matrix are either real or complex. Estimates for the computational work required to reduce theL 2 norm of the error by a specified factor ɛ are also given.
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    URL: http://dx.doi.org/10.1007/BF01396653
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  • 18
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    On fixed point linear equations (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 53-59 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; 47B55 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary By means of successive partial substitutions it is possible to obtain new fixed point linear equations from old ones and it is interesting to determine how the spectral radius of the corresponding matrices varies. We prove that, when the original matrix is nonnegative, this variation is decreasing or increasing, depending on whether the original matrix has its spectral radius smaller or greater than 1. We answer in this way a question posed by F. Robert in [5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395808
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  • 19
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    A modified bisection algorithm for the determination of the eigenvalues of a symmetric tridiagonal matrix (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 417-419 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A modification to the well known bisection algorithm [1] when used to determine the eigenvalues of a real symmetric matrix is presented. In the new strategy the terms in the Sturm sequence are computed only as long as relevant information on the required eigenvalues is obtained. The resulting algorithm usingincomplete Sturm sequences can be shown to minimise the computational work required especially when only a few eigenvalues are required. The technique is also applicable to other computational methods which use the bisection process.
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    URL: http://dx.doi.org/10.1007/BF01396441
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  • 20
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    A contribution to the theory of condition (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 85-96 
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    ISSN: 0945-3245
    Keywords: AMS65F05 ; 65F 15 ; 65F 20 ; 65F 35 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the use of the condition number of a problem, as defined by Rice in 1966, is discussed. For the eigenvalue, eigenvector, and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived.
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    URL: http://dx.doi.org/10.1007/BF01399313
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  • 21
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    Inversion of tridiagonal matrices (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 333-345 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 15 A 09, 15-04 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist. Ukita's theorem is extended to characterize the class of matrices that have tridiagonal inverses.
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    URL: http://dx.doi.org/10.1007/BF01396436
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  • 22
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    On the convergence of the symmetric SOR method for matrices with red-black ordering (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 113-117 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We prove that if the matrixA has the structure which results from the so-called “red-black” ordering and ifA is anH-matrix then the symmetric SOR method (called the SSOR method) is convergent for 0〈ω〈2. In the special case thatA is even anM-matrix we show that the symmetric single-step method cannot be accelerated by the SSOR method. Symmetry of the matrixA is not assumed.
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    URL: http://dx.doi.org/10.1007/BF01399315
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  • 23
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    Zur Konvergenz eines Verfahrens von D.J. Evans zur iterativen Verbesserung einer Näherung für die inverse Matrix (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 163-173 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Recently D.J. Evans introduced an implicit matrix inversion process showing asymptotic behaviour which is superior to that of the well known Schulz-method. In this paper we give sufficient conditions for convergence, prove some error bounds and show that under certain conditions the iterates are converging monotonously.
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    URL: http://dx.doi.org/10.1007/BF01408691
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  • 24
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    The lognormal approach to predicting local distributions of selective mining unit grades (1980)
    Springer
    Mathematical geology 12 (1980), S. 285-303 
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    ISSN: 1573-8868
    Keywords: geostatistics ; lognormal distribution ; mine planning ; ore reserve estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When planning highly selective mining operations, the challenge is to estimate mineable ore reserves that will be selected at the mining stage. From exploration data it is not possible to estimate accurately the grade (or thickness) of each future selective mining unit; however, it is possible to estimate the local distributions of these mining unit grades within large panels suitable for long-range mine planning. Application of a cut-off then allows estimation of the recovered ore tonnage and grade within each such panel. Derivation of local conditional distributions is rather simple when the grade is either normally or lognormally distributed. The geologically important lognormal case is fully described both in the stationary and the nonstationary case. Cross validations of these techniques using the exploration data of the Imouraren uranium deposit are presented.
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    URL: http://dx.doi.org/10.1007/BF01029417
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  • 25
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    The random coin method: Solution of the problem of the simulation of a random function in the plane (1980)
    Springer
    Mathematical geology 12 (1980), S. 25-32 
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    ISSN: 1573-8868
    Keywords: random function ; geostatistics ; simulation ; covariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new geostatistical method to obtain realizations of stationary random functions in the plane.
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    URL: http://dx.doi.org/10.1007/BF01039901
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  • 26
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    Disjunctive kriging: Comparison of theory with actual results (1980)
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    Mathematical geology 12 (1980), S. 305-320 
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    ISSN: 1573-8868
    Keywords: disjunctive kriging ; logarithmic kriging ; gold evaluation ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The method of disjunctive kriging is applied to the evaluation of blocks of ore in a gold mine, and the estimated block values are compared with the true block values. First the theory of disjunctive kriging as applicable to mine valuation is presented from the user's viewpoint. The theory is then applied to process sample values originating from a large gold mine. Using the computer simulation of a number of sampling programs, estimated values and true values are compared. The disjunctive kriging estimates are also compared with estimates obtained by other methods of evaluation, including logarithmic kriging. It is shown that the results obtained, using real world data, are in complete agreement with the results expected according to the geostatistical theory.
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    URL: http://dx.doi.org/10.1007/BF01029418
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  • 27
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    Statistical and geostatistical methods applied to the exploration work of the Nanisivik Zn-Pb mine, Baffin Island, Canada (1980)
    Springer
    Mathematical geology 12 (1980), S. 321-337 
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    ISSN: 1573-8868
    Keywords: geostatistics ; kriging ; variogram analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Nanisivik Pb-Zn deposit at Strathcona Sound, northern Baffin Island, Canada, is an orebody that is an S-shaped lens 3000 m long, 75 m wide, and 2–20 m thick. It is an epigenetic karst channel filling. Total reserves are 6.9 million short tons of 14.12% Zn, 1.4% Pb, and 1.77 oz of Ag per ton. The mine was brought into production in 1976 at a rate of 2000 short tons per day. In the preproduction phase variogram studies based only on surface holes indicated a random distribution. For the evaluation of grades and for the determination of the confidence limits, classic statistical procedures were applied. Since the drilling density was different in different ore zones, a model was developed to test the effect of different drill hole spacings on the uncertainties in the present value in a discounted cash flow model. After the initial development and mining stage, structures could be recognized in semivariograms. Studies for a best drilling grid showed that the pattern of 25 ×20 m used in the mine could be extended to 35 ×35 m, taking into account that eight stopes are mined simultaneously. For ore reserve calculations weighing factors were calculated by kriging for six universally applicable geometric situations. Only the drill holes within a block and immediately surrounding it were taken into account. A test in a well-known zone yielded satisfactory results. A test to predict highs and lows of the grade accurately enough to optimally place the pillars failed.
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    URL: http://dx.doi.org/10.1007/BF01029419
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  • 28
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    The effect of drift on the experimental semivariogram (1982)
    Springer
    Mathematical geology 14 (1982), S. 309-319 
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    ISSN: 1573-8868
    Keywords: Bias ; drift ; semivariogram ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When nonlinear drift is present, the nature of the bias in the experimental semivariogram estimator of the semivariogram function is determined by the extent and density of the sampling as well as by the drift function itself. The bias caused by drift may affect the interpretation of the experimental semivariogram over its entire range.
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    URL: http://dx.doi.org/10.1007/BF01032592
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    Prediction of local ore recoveries and ore-waste ratios at the silver bell uranium mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 645-660 
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    ISSN: 1573-8868
    Keywords: geostatistics ; uranium ; production forecast
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.
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    URL: http://dx.doi.org/10.1007/BF01033885
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    The combination of sampling and kriging in the regional estimation of coal resources (1982)
    Springer
    Mathematical geology 14 (1982), S. 87-106 
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    ISSN: 1573-8868
    Keywords: coal ; geostatistics ; kriging ; regional estimation ; systematic sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.
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    URL: http://dx.doi.org/10.1007/BF01083946
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    Exact formulas for approximating variogram function integrals (1980)
    Springer
    Mathematical geology 12 (1980), S. 577-588 
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    ISSN: 1573-8868
    Keywords: variogram ; geostatistics ; estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.
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    URL: http://dx.doi.org/10.1007/BF01034745
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    On the estimation of the generalized covariance function (1982)
    Springer
    Mathematical geology 14 (1982), S. 57-64 
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    ISSN: 1573-8868
    Keywords: estimation ; generalized covariance function ; generalized increments ; geostatistics ; intrinsic random functions ; multicollinearity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables.
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    URL: http://dx.doi.org/10.1007/BF01037447
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    Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body (1982)
    Springer
    Mathematical geology 14 (1982), S. 557-564 
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    ISSN: 1573-8868
    Keywords: geostatistics ; variogram ; outliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
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    URL: http://dx.doi.org/10.1007/BF01033879
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    Anisotropic hole-effect modeling (1982)
    Springer
    Mathematical geology 14 (1982), S. 217-239 
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    ISSN: 1573-8868
    Keywords: geostatistics ; variograms ; anisotropies ; tungsten
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The regionalization of tungsten grades at the χ deposit represents an ideal case for anisotropic hole-effect variogram modeling. The modeling technique is presented step by step and the consequences of the model on block kriging are indicated.
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    URL: http://dx.doi.org/10.1007/BF01032885
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    Sequential sampling to contour an uncertain function (1982)
    Springer
    Mathematical geology 14 (1982), S. 387-404 
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    ISSN: 1573-8868
    Keywords: geostatistics ; resource estimation ; geoexploration ; sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.
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    URL: http://dx.doi.org/10.1007/BF01077529
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    Geostatistical case studies of the advantages of lognormal-de Wijsian kriging with mean for a base metal mine and a gold mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 547-555 
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    ISSN: 1573-8868
    Keywords: geostatistics ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.
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    URL: http://dx.doi.org/10.1007/BF01033878
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    A new augmented Lagrangian function for inequality constraints in nonlinear programming problems (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 495-519 
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    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear programming ; Numerical methods ; computational methods ; augmented Lagrangian functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a new augmented Lagrangian function is introduced for solving nonlinear programming problems with inequality constraints. The relevant feature of the proposed approach is that, under suitable assumptions, it enables one to obtain the solution of the constrained problem by a single unconstrained minimization of a continuously differentiable function, so that standard unconstrained minimization techniques can be employed. Numerical examples are reported.
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    URL: http://dx.doi.org/10.1007/BF00940544
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    Equivalence theorem for constrained optimization of the LegendreK-transform of a concave function (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 25-31 
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    ISSN: 1573-2878
    Keywords: Optimization ; Kuhn-Tucker theorem ; LegendreK-transform ; equilibrium composition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The most common way of determining the steady states of a system is through the optimization of a concave function on a convex set. This applies only to cases where the objective function depends exclusively onextensive variables. In fields such as econometrics, physics, or chemistry, controllable quantities (and therefore constrained variables) are generally referred to asintensive parameters, and the states are described through a potential function. In the following pages, we examine how these two aspects can be connected.
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    An approach to the solution of the vector optimization problem of dynamic systems (1982)
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    Journal of optimization theory and applications 38 (1982), S. 409-422 
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    ISSN: 1573-2878
    Keywords: Optimization ; scalar optimization ; vector optimization ; optimization under vector-valued criteria ; maximum principle ; dynamic programming ; optimization of dynamic systems ; multi-criteria decision problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.
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    URL: http://dx.doi.org/10.1007/BF00935346
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    System theory: A new approach to wave mechanics (1980)
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    Journal of optimization theory and applications 32 (1980), S. 463-478 
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    ISSN: 1573-2878
    Keywords: Optimization ; control ; relativity ; stochastic processes ; wave mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The intention of this paper is to show how the influence of the work of Bellman has initiated a tentative new approach to quantum mechanics
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    Die Wahl der Trägergasgeschwindigkeit bei der Analyse von Mehrkomponenten-Gemischen (1980)
    Springer
    Chromatographia 13 (1980), S. 61-67 
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    ISSN: 1612-1112
    Keywords: Optimization ; Carrier gas velocity ; Gas chromatography ; Influence of temperature on optimum velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Zusammenfassung Die Wahl der mittleren, linearen Trägergasgeschwindigkeit bei der Analyse von Mehrkomponentengemischen unter isothermen und temperaturprogrammierten Bedingungen wird diskutiert. Es wird gezeigt, daß stets eine Trägergasgeschwindigkeit gewählt werden sollte, die mindestens gleich, besser jedoch höher ist, als die optimale Gasgeschwindigkeit für den ersten Peak, gemessen bei der Starttemperatur (Temperaturprogramm) oder bei der eingestellten Ofentemperatur (isotherme Fahrweise).
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    URL: http://dx.doi.org/10.1007/BF02302719
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    A simple procedure for the rapid optimization of reversed-phase separations with ternary mobile phase mixtures (1982)
    Springer
    Chromatographia 15 (1982), S. 688-696 
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    ISSN: 1612-1112
    Keywords: Reversed-phase LC ; Ternary mobile-phases ; Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A simple rapid procedure is described for estimating optimum compositions of ternary mobile phase mixtures for the separation of samples by reversed-phase liquid chromatography (RPLC). Retention data in two iso-eluotropic binary mobile phase mixtures (mixtures with equal retention times) are required to initiate the procedure. The logarithm of the capacity factor is assumed to vary linearly with the composition of isoeluotropic ternary mixtures formed by mixing the two limiting binaries. Using the product of resolution factors of adjacent peaks as the criterion, an optimum ternary composition is then calculated. After a chromatogram has been obtained with the predicted optimum ternary mobile phase, the procedure is repeated until no further improvement can be achieved. Examples of the application of the present procedure are described to illustrate its effectiveness.
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    URL: http://dx.doi.org/10.1007/BF02261886
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    Fast analysis by gas chromatography (1982)
    Springer
    Chromatographia 15 (1982), S. 125-132 
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    ISSN: 1612-1112
    Keywords: Capillary columns ; Fast analysis ; Gas chromatography ; Instrumental effects ; Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The efficiency of fast GC columns depends largely on the quality of the chromatograph. A theoretical and experimental study shows the relative importance of the various phenomena involved and permits the optimization of a GC System. Extremely good performances, exceeding 2,500 plates per second have been routinely obtained.
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    A chromatographic response function for automated optimization of separations (1982)
    Springer
    Chromatographia 15 (1982), S. 498-504 
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    ISSN: 1612-1112
    Keywords: Analytical performance ; Chromatographic response function ; HPLC (or LC) ; Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A chromatographic response function is studied that is sensitive to important criteria of analytical performance: selectivity, accuracy, precision and time required to perform the separation. This function can be applied to mixtures of unknown solutes and little computational effort is needed to evaluate the numerical value of the function from the chromatogram. It shows well defined optima at elution strengths that give minimal elution times simultaneously with good separations in high-performance liquid chromatography. No prior chromatographic information characterizing the expected performance of a system is required. It is possible to use this function without a mechanistic model describing the separation process.
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    URL: http://dx.doi.org/10.1007/BF02260283
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    An improved optimization procedure for the selection of mixed mobile phases in reversed phase liquid chromatography (1982)
    Springer
    Chromatographia 16 (1982), S. 48-52 
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    ISSN: 1612-1112
    Keywords: RP-HPLC ; Optimization ; Complex mobile phases ; Iso-eluotropic mixtures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The stepwise procedure described previously [1] for the selection of optimal mobile phase compositions in reversed phase liquid chromatography (RPLC) is improved in two ways. The optimization criterion is modified to account for variations in analysis time. The iterative approach to the optimal solvent composition makes a more efficient use of previous data. An example illustrates the resulting gain in speed and accuracy.
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    URL: http://dx.doi.org/10.1007/BF02258868
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    On the convergence, invariance, and related aspects of a modification of Huang's algorithm (1982)
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    Journal of optimization theory and applications 37 (1982), S. 315-341 
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    ISSN: 1573-2878
    Keywords: Optimization ; unconstrained minimization ; updates ; line searches ; convergence ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a certain generalization of the Huang family of updates and discuss, firstly, convergence, dependence on parameters, and descent property; secondly, invariance under nonlinear scaling, conjugacy of search directions, and possibility of achieving a better approximation of the inverse of the Hessian. The last three aspects are shown to be dependent on particular choices of parameters. A numerical experiment is presented comparing the performances of the usual and modified BFGS algorithms.
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    URL: http://dx.doi.org/10.1007/BF00935273
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