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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.

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Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
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by Francis J. Narcowich and Joseph D. Ward PDF
Math. Comp. 63 (1994), 661-687 Request permission

Abstract:

In this paper, we consider a broad class of interpolation problems, for both scalar- and vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation problems are well poised; that is, the interpolation matrices are invertible. As a sample result, we show that a divergence-free vector field can be interpolated by a linear combination of convolutions of the data-generating distributions with a divergence-free, $3 \times 3$ matrix-valued conditionally positive definite function. In addition, we obtain norm estimates for inverses of interpolation matrices that arise in a class of multivariate Hermite interpolation problems.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 661-687
  • MSC: Primary 41A05; Secondary 41A63
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1254147-6
  • MathSciNet review: 1254147