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Lecture-15 - Lecture-15 Homework Rate of Convergence of CG...

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1 Lecture-15 Homework, Rate of Convergence of CG, preconditioning, FR-GC, PR-GC Homework (Due April 17) • 5.1 • 5.9 Proof for Theorem 5.5 (see the slides)
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2 Theorem 5.4 If A has only r distinct eigenvalues, then the CG iteration will terminate at the solution in at most r iterations. Theorem 5.5 2 * 0 2 1 1 2 * 1 || || || || A k n k n A k x x x x - + - - - - + l l l l If A has eigenvalues we have n l l l K 2 1 n k n k n l l l l , , , , , 1 1 K K + - - Eigenvalues
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