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Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems
Sun, Weiwei Huang, Weizhang Russell, Robert D.
Sun, Weiwei
Huang, Weizhang
Russell, Robert D.
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Abstract
A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral condition numbers of the preconditioned collocation matrices are bounded by constants independent of the number of mesh nodes when certain exact low-order finite difference preconditionings are used. Preconditioners based on incomplete LU factorization are also discussed. Numerical experiments show the efficiency and robustness of the preconditioning.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S0036142993249760.
Date
1996-12-01
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Society for Industrial and Applied Mathematics
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Keywords
collocation, preconditioning, boundary value problem
Citation
Sun, Weiwei., Huang, Weizhang., Russell, Robert D. "Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems." SIAM J. Numer. Anal., 33(6), 2268–2285. (18 pages). http://dx.doi.org/10.1137/S0036142993249760.