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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Improved condition number for spectral methods
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by Wilhelm Heinrichs PDF
Math. Comp. 53 (1989), 103-119 Request permission

Abstract:

For the known spectral methods (Galerkin, Tau, Collocation) the condition number behaves like $O({N^4})$ (N: maximal degree of polynomials). We introduce a spectral method with an $O({N^2})$ condition number. The advantages with respect to propagation of rounding errors and preconditioning are demonstrated. A direct solver for constant coefficient problems is given. Extensions to variable coefficient problems and first-order problems are discussed. Numerical results are presented, showing the effectiveness of our methods.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 103-119
  • MSC: Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0972370-0
  • MathSciNet review: 972370