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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Numerical differentiation and the solution of multidimensional Vandermonde systems
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by G. Galimberti and V. Pereyra PDF
Math. Comp. 24 (1970), 357-364 Request permission

Abstract:

We define multidimensional Vandermonde matrices (MV) to be certain submatrices of Kronecker products of standard Vandermonde matrices. These MV matrices appear naturally in multidimensional problems of polynomial interpolation. An explicit algorithm is produced to solve systems of linear equations with MV matrices of coefficients. This is an extension of work of Stenger for the two-dimensional case. Numerical results for three-dimensional numerical differentiation are given.
References
    Å. Björck & V. Pereyra, "Solution of Vandermonde systems of equations," Publ. 70-02, Dept. Comp., Fac. Ci. Univ. Cent. Venezuela.
  • Frank Stenger, Kronecker product extensions of linear operators, SIAM J. Numer. Anal. 5 (1968), 422–435. MR 235711, DOI 10.1137/0705033
    • M. Stoyakovich, "Inversion of the matrices encountered in relay switching circuit synthesis theory," Ž. Vyčisl. Mat. i Mat. Fiz., v. 6, 1966, pp. 158 161.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 357-364
  • MSC: Primary 65.55
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0275668-2
  • MathSciNet review: 0275668