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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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Approximation results for orthogonal polynomials in Sobolev spaces
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by C. Canuto and A. Quarteroni PDF
Math. Comp. 38 (1982), 67-86 Request permission

Abstract:

We analyze the approximation properties of some interpolation operators and some $L_\omega ^2$-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight function $\omega ({x_1}, \ldots ,{x_d})$, $d \geqslant 1$. The error estimates for the Legendre system and the Chebyshev system of the first kind are given in the norms of the Sobolev spaces $H_\omega ^s$. These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 67-86
  • MSC: Primary 41A10
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0637287-3
  • MathSciNet review: 637287