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Numerical differentiation and the solution of multidimensional Vandermonde systems


Authors: G. Galimberti and V. Pereyra
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
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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 [Enhancements On Off] (What's this?)

  • [1] Å. Björck & V. Pereyra, "Solution of Vandermonde systems of equations," Publ. 70-02, Dept. Comp., Fac. Ci. Univ. Cent. Venezuela.
  • [2] Frank Stenger, Kronecker product extensions of linear operators, SIAM J. Numer. Anal. 5 (1968), 422–435. MR 0235711, https://doi.org/10.1137/0705033
  • [3] 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

DOI: https://doi.org/10.1090/S0025-5718-1970-0275668-2
Keywords: Multidimensional Vandermonde matrices, numerical differentiation, Kronecker products, Vandermonde systems of equations
Article copyright: © Copyright 1970 American Mathematical Society