Improved condition number for spectral methods
Author:
Wilhelm Heinrichs
Journal:
Math. Comp. 53 (1989), 103-119
MSC:
Primary 65N30
DOI:
https://doi.org/10.1090/S0025-5718-1989-0972370-0
MathSciNet review:
972370
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Abstract | References | Similar Articles | Additional Information
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
Keywords:
Spectral methods,
condition number,
direct solver,
iterative methods,
elliptic problems,
first-order problems
Article copyright:
© Copyright 1989
American Mathematical Society