On the norms of inverses of pseudospectral differentiation matrices

D.M. Sloan

doi:10.1137/S0036142902414542

On the norms of inverses of pseudospectral differentiation matrices

D.M. Sloan

Mathematics And Statistics

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2 Citations (Scopus)

Abstract

In this paper we give integral expressions for the elements of the inverses of second-order pseudospectral differentiation matrices. Simple upper bounds are given for the maximum norms of these inverse matrices when Chebyshev collocation points are used. Comment is made on the failure to obtain upper bounds that are uniform in the number of collocation points when the points are evenly spaced. We also give integral expressions for inverses of first-order Chebyshev pseudospectral differentiation matrices.

Original language	English
Pages (from-to)	30-48
Number of pages	18
Journal	SIAM Journal on Numerical Analysis
Volume	42
Issue number	1
DOIs	https://doi.org/10.1137/S0036142902414542
Publication status	Published - 2004

Keywords

pseudospectral
differentiation matrices
Chebyshev

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10.1137/S0036142902414542

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abstract = "In this paper we give integral expressions for the elements of the inverses of second-order pseudospectral differentiation matrices. Simple upper bounds are given for the maximum norms of these inverse matrices when Chebyshev collocation points are used. Comment is made on the failure to obtain upper bounds that are uniform in the number of collocation points when the points are evenly spaced. We also give integral expressions for inverses of first-order Chebyshev pseudospectral differentiation matrices.",

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AU - Sloan, D.M.

PY - 2004

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N2 - In this paper we give integral expressions for the elements of the inverses of second-order pseudospectral differentiation matrices. Simple upper bounds are given for the maximum norms of these inverse matrices when Chebyshev collocation points are used. Comment is made on the failure to obtain upper bounds that are uniform in the number of collocation points when the points are evenly spaced. We also give integral expressions for inverses of first-order Chebyshev pseudospectral differentiation matrices.

AB - In this paper we give integral expressions for the elements of the inverses of second-order pseudospectral differentiation matrices. Simple upper bounds are given for the maximum norms of these inverse matrices when Chebyshev collocation points are used. Comment is made on the failure to obtain upper bounds that are uniform in the number of collocation points when the points are evenly spaced. We also give integral expressions for inverses of first-order Chebyshev pseudospectral differentiation matrices.

KW - pseudospectral

KW - differentiation matrices

KW - Chebyshev

UR - http://dx.doi.org/10.1137/S0036142902414542

U2 - 10.1137/S0036142902414542

DO - 10.1137/S0036142902414542

M3 - Article

VL - 42

SP - 30

EP - 48

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 1

ER -

On the norms of inverses of pseudospectral differentiation matrices

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Keywords

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