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  • Articles  (17)
  • CR: 5.14  (17)
  • 2020-2022
  • 1975-1979  (17)
  • 1950-1954
  • Mathematics  (17)
  • Geosciences
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  • Articles  (17)
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  • Mathematics  (17)
  • Geosciences
  • 1
    Electronic Resource
    Electronic Resource
    Rank-one modification of the symmetric eigenproblem (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 31-48 
    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 presented for computing the eigensystem of the rank-one modification of a symmetric matrix with known eigensystem. The explicit computation of the updated eigenvectors and the treatment of multiple eigenvalues are discussed. The sensitivity of the computed eigenvectors to errors in the updated eigenvalues is shown by a perturbation analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396012
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  • 2
    Electronic Resource
    Electronic Resource
    Updating the singular value decomposition (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 111-129 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F30 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary LetA be anm×n matrix with known singular value decomposition. The computation of the singular value decomposition of a matrixà is considered, whereà is obtained by appending a row or a column toA whenm≧n or by deleting a row or a column fromA whenm〉n. An algorithm is also presented for solving the updated least squares problemà y−b≈, obtained from the least squares problemAx−b by appending an equation, deleting an equation, appending an unknown, or deleting an unknown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397471
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  • 3
    Electronic Resource
    Electronic Resource
    Convergent nonnegative matrices and iterative methods for consistent linear systems (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 265-279 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 F 10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we study linear stationary iterative methods with nonnegative iteration matrices for solving singular and consistent systems of linear equationsAx=b. The iteration matrices for the schemes are obtained via regular and weak regular splittings of the coefficients matrixA. In certain cases when only some necessary, but not sufficient, conditions for the convergence of the iterations schemes exist, we consider a transformation on the iteration matrices and obtain new iterative schemes which ensure convergence to a solution toAx=b. This transformation is parameter-dependent, and in the case where all the eigenvalues of the iteration matrix are real, we show how to choose this parameter so that the asymptotic convergence rate of the new schemes is optimal. Finally, some applications to the problem of computing the stationary distribution vector for a finite homogeneous ergodic Markov chain are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397879
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  • 4
    Electronic Resource
    Electronic Resource
    A new method for the solution ofAx=b (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 287-289 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65FO5 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An alternative to Gauss elimination is developed to solveAx=b. The method enables one to exploit zeros in the lower triangle ofA, so that the number of multiplications needed to perform the algorithm can be substantially reduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389213
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  • 5
    Electronic Resource
    Electronic Resource
    Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 183-208 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An iteration based upon the Tchebychev polynomials in the complex plane can be used to solve large sparse nonsymmetric linear systems whose eigenvalues lie in the right half plane. The iteration depends upon two parameters which can be chosen from knowledge of the convex hull of the spectrum of the linear operator. This paper deals with a procedure based upon the power method for dynamically estimating the convex hull of the spectrum. The stability of the procedure is discussed in terms of the field of values of the operator. Results show the adaptive procedure to be an effective method of determining parameters. The Tchebychev iteration compares favorably with several competing iterative methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397475
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  • 6
    Electronic Resource
    Electronic Resource
    Alternating methods for sets of linear equations (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 105-108 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A generalization of alternating methods for sets of linear equations is described and the number of operations calculated. It is shown that the lowest number of arithmetic operations is achieved in the SSOR algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397654
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  • 7
    Electronic Resource
    Electronic Resource
    A factorization method for the solution of constrained linear least squares problems allowing subsequent data changes (1978)
    Springer
    Numerische Mathematik 31 (1978), S. 431-463 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F20, 90C05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we describe how to use Gram-Schmidt factorizations of Daniel et al. [1] to realize the method of [8] for solving linearly constrained linear least squares problems. The main advantage of using these factorizations is that it is relatively easy to take data changes into account, if necessary. The algorithm is compared numerically with two other codes, one of them published by Lawson and Hanson [3]. Further computational tests show the efficiency of the proposed methods, if a few data of the original problem are changed subsequently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404569
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  • 8
    Electronic Resource
    Electronic Resource
    On a new class of elementary matrices (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 173-180 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new class of elementary matrices, a block-generalisation of plane rotations, is presented and the application in constructing quadratically convergent block diagonalisation algorithms of Jacobi type is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399552
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  • 9
    Electronic Resource
    Electronic Resource
    On a class of Jacobi-like procedures for diagonalising arbitrary real matrices (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 157-172 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new class of elementary matrices is presented which are convenient in Jacobi-like diagonalisation methods for arbitrary real matrices. It is shown that the presented transformations possess the normreducing property and that they produce an ultimate quadratic convergence even in the case of complex eigenvalues. Finally, a quadratically convergent Jacobi-like algorithm for real matrices with complex eigenvalues is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399551
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  • 10
    Electronic Resource
    Electronic Resource
    A quadratically convergent Jacobi-like method for real matrices with complex eigenvalues (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 425-435 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A real Jacobi-like algorithm for diagonalizing arbitrary real matrices with complex eigenvalues is described and its applicability discussed. Numerical results are given and compared with those of the well-known real and complex algorithm of Eberlein.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399324
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