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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.

 

Gauss interpolation formulas and totally positive kernels
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by David L. Barrow PDF
Math. Comp. 31 (1977), 984-993 Request permission

Abstract:

This paper simplifies and generalizes an earlier result of the author’s on Gauss interpolation formulas for the one-dimensional heat equation. Such formulas approximate a function at a point $({x^\ast },{t^\ast })$ in terms of a linear combination of its values on an initial-boundary curve in the (x, t) plane. The formulas are characterized by the requirement that they be exact for as many basis functions as possible. The basis functions are generated from a Tchebycheff system on the line $t = 0$ by an integral kernel $K(x,y,t)$, in analogy with the way heat polynomials are generated from the monomials ${x^i}$ by the fundamental solution to the heat equation. The total positivity properties of $K(x,y,t)$ together with the theory of topological degree are used to establish the existence of the formulas.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 984-993
  • MSC: Primary 65N99
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0483560-X
  • MathSciNet review: 0483560