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Mathematics of Computation

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



Improved condition number for spectral methods

Author: Wilhelm Heinrichs
Journal: Math. Comp. 53 (1989), 103-119
MSC: Primary 65N30
MathSciNet review: 972370
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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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Keywords: Spectral methods, condition number, direct solver, iterative methods, elliptic problems, first-order problems
Article copyright: © Copyright 1989 American Mathematical Society