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Unformatted text preview: ing point operations (K ops), and the residual and error in L2 for GMRES procedures with and without preconditioners (Example 9.4.3). The results with preconditioning are much better than those without. The restarted and incomplete orthogonalization versions of GMRES have comparable performance. Likewise, the SSOR and ILU(0) preconditionings are comparable. Problems ~ 1. With A being positive de nite and symmetric, show that solutions x of (9.4.5c) minimizes (9.4.5a), and conversely. 68 Solution Techniques for Elliptic Problems Bibliography 1] J.A. George. Nested dissection of a regular nite element mesh. SIAM Journal on Numerical Analysis, 10:345{363, 1973. 2] J.A. George and J.W. Liu. Computational Solution of Large Sparse Positive De nite Systems. Prentice-Hall Series in Automatic Computation. Prentice-Hall, Englewood Cli s, 1981. 3] E. Isaacson and H.B. Keller. Analysis of Numerical Methods. John Wiley and Sons, New York, 1966. 4] Y. Saad. Iterative Methdos for Sparse Linear Systems. PWS, Boston, 1996. 5] J.C. Strikwerda. Finite Di erence Schemes and Partial Di erential Equations. Chapman and Hall, Paci c Grove, 1989. 6] R.S. Varga. Matrix Iterative Analysis. Prentice-Hall, Englewood Cli s, 1963. 7] E. L. Wachpress. Iterative Solution of Elliptic Systems. Prentice-Hall, Englewood Cli s, 1966. 69...
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This document was uploaded on 03/16/2014 for the course CSCI 6840 at Rensselaer Polytechnic Institute.

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