On the norms of inverses of pseudospectral differentiation matrices

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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.
Original languageEnglish
Pages (from-to)30-48
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume42
Issue number1
DOIs
Publication statusPublished - 2004

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Keywords

  • pseudospectral
  • differentiation matrices
  • Chebyshev

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