Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems

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Issue Date
1996-12-01Author
Sun, Weiwei
Huang, Weizhang
Russell, Robert D.
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
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Show full item recordAbstract
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.
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This is the published version, also available here: http://dx.doi.org/10.1137/S0036142993249760.
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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.
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