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  • Articles  (11)
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  • AMS(MOS): 65D15  (6)
  • geostatistics  (5)
  • 1980-1984  (11)
  • 1984  (11)
  • Mathematics  (11)
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  • Articles  (11)
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  • 1980-1984  (11)
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  • 1
    Electronic Resource
    Electronic Resource
    Padé-type approximants of exp (−z) whose denominators are (1+z/n) n (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 283-292 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we show that the sequences of Padé-type approximants (k−1/k) and (k/k) converge to exp (−z), uniformly and geometrically on every compact subset of the plane. A numerical study has been done, which discriminates these sequences from the point of view ofA-acceptability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390128
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  • 2
    Electronic Resource
    Electronic Resource
    Best constants occuring with the modulus of continuity in the error estimate for spline interpolants of odd degree on equidistant grids (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 407-415 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We deal with spline interpolants of odd degree on equidistant grids. The main interest is directed on cardinal and onn-periodic interpolation, wheren is odd. By the aid of an explicit representation of the interpolant by Euler-Frobenius-polynomials, we calculate the minimal constant occuring in the error estimate with the modulus of continuity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405571
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  • 3
    Electronic Resource
    Electronic Resource
    General order Newton-Padé approximants for multivariate functions (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 293-307 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x 1, ...,x p ). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390129
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  • 4
    Electronic Resource
    Electronic Resource
    Error estimates for spline interpolants on equidistant grids (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 417-424 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For oddm, the error of them-th-degree spline interpolant of power growth on an equidistant grid is estimated. The method is based on a decomposition formula for the spline function, which locally can be represented as an interpolation polynomial of degreem which is corrected by an (m+1)-st.-order difference term.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405572
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  • 5
    Electronic Resource
    Electronic Resource
    Die Struktur der normalen rationalen Funktionen (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 379-388 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; 41A20 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We determine the connected components of the set of normal elements of the family ℛ m n [a,b] of rational functions. Numerical difficulties occuring with the computation of the Chebyshev approximation via the Remez algorithm can be caused by its disconnectedness. In order to illustrate this we give numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390180
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  • 6
    Electronic Resource
    Electronic Resource
    Discrete approximations to spherically symmetric distributions (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 53-60 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5. 13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the approximation of spherically symmetric distributions in ℝ d by linear combinations of Heaviside step functions or Dirac delta functions. The approximations are required to faithfully reproduce as many moments as possible. We discuss stable methods of computing such approximations, taking advantage of the close connection with Gauss-Christoffel quadrature. Numerical results are presented for the distributions of Maxwell, Bose-Einstein, and Fermi-Dirac.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389754
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  • 7
    Electronic Resource
    Electronic Resource
    Comparison of geostatistical calculations with the results of open pit mining at the Iharkut bauxite district, Hungary: A case study (1984)
    Springer
    Mathematical geology 16 (1984), S. 173-191 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; reserve evaluation ; bauxite prospecting ; open-pit mining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical calculations were carried out on two completely exhausted open-pit bauxite mines in the Iharkut bauxite district, Hungary. Fictitious regular drilling grids were laid on the maps, and horizontal variograms were calculated for drilling grids evaluating the bauxite surface, footwall surface, and bauxite thickness. Point kriging was carried out for all three parameters. Bauxite reserves were calculated using block kriging for bauxite thickness. The total estimation variance of the reserves has been established. Results were compared with real reserves obtained from the mine maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032215
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  • 8
    Electronic Resource
    Electronic Resource
    Conditional estimation variances: An empirical approach (1984)
    Springer
    Mathematical geology 16 (1984), S. 327-350 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; estimation variance ; recoverable reserves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract One of the tasks routinely carried out by geostatisticians is the evaluation of global mining reserves corresponding to a given cutoff grade and size of selective mining units. A long with these recovery figures, the geostatistician generally provides an assessment of the global estimation variance, which represents the precision of the overall average grade estimate, when no cutoff is applied. Such a global estimation variance is of limited interest for evaluating mining projects; what is required is the reliability of the estimate of recovered reserves or, in other words, the conditional estimation variance. Unfortunately, classical linear geostatistical methods fail to provide an easy way to estimate this variance. Through the use of simulated deposits (representing various types of regionalization)the present paper reviews and discusses the effects of changes in cutoff grade and selective mining unit size on the conditional estimation variance. It is shown that, when the cutoff grade is applied to a pointsupport (sample-size)distribution, the conditional estimation variance appears to be readily accessible by classical formulas, once the conditional semivariogram is known. However, the evaluation of the conditional estimation variance seems to be less straightforward for the general case when a cutoff is applied to the average grade distribution of selective mining units. Empirical approximation formulas for the conditional estimation variance are tentatively proposed, and their performance in the case of the simulated deposits is shown. The limitations of these approximations are discussed, and possible ways of formalizing the problem suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029885
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  • 9
    Electronic Resource
    Electronic Resource
    Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)
    Springer
    Mathematical geology 16 (1984), S. 19-35 
    Details
    ISSN: 1573-8868
    Keywords: groundwater ; geostatistics ; cokriging ; kriging ; transmissivity ; specific capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036238
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  • 10
    Electronic Resource
    Electronic Resource
    Kriging in a global neighborhood (1984)
    Springer
    Mathematical geology 16 (1984), S. 249-265 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; moving neighborhood ; global neighborhood ; geostatistics ; automatic contouring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The kriging estimator is usually computed in a moving neighborhood; only the data near the point to be estimated are used. This moving neighborhood approach creates discontinuities in mapping applications. An alternative approach is presented here, whereby all points are estimated using all the available data. To solve the resulting large linear system the kriging estimator is expressed in terms of the inverse of the covariance matrix. The covariance matrix has the advantage of being positive definite and the size of system which can be solved without encountering numerical instability is substantially increased. Because the kriging matrix does not change, the estimator can be written in terms of scalar products, thus avoiding the more time-consuming matrix multiplications of the standard approach. In the particular case of a covariance which is zero for distances greater than a fixed value (the range), the resulting banded structure of the covariance matrix is shown to lead to substantial computational savings in both run time and storage space. In this case the calculation time for the kriging variance is also substantially reduced. The present method is extended to the nonstationary case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032690
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