CgIntro - Administrivia Administrivia Homework 4 on web...

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Administrivia: October 28, 2008 Administrivia: October 28, 2008 Homework 4 on web site, due next Wednesday. Read sec. 1-12 of Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain.” Final project proposals due Nov. 11: Survey paper Algorithms experiment Application experiment List of project suggestions and due dates on web site.
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The Landscape of Sparse Ax=b Solvers The Landscape of Sparse Ax=b Solvers Pivoting LU GMRES , BiCGSTAB , Cholesky Conjugate gradient Direct A = LU Iterative y’ = Ay Non- symmetric Symmetric positive definite More Robust Less Storage More Robust More General D
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Four views of the conjugate gradient method Four views of the conjugate gradient method To solve Ax = b, where A is symmetric and positive definite. 1. Operational view 2. Orthogonal sequences view 3. Optimization view 4. Convergence view
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Four views of the conjugate gradient method Four views of the conjugate gradient method To solve Ax = b, where A is symmetric and positive definite. 1. Operational view 2. Orthogonal sequences view 3. Optimization view 4. Convergence view
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Conjugate gradient iteration for Ax = b Conjugate gradient iteration for Ax = b x 0 = 0 approx solution r 0 = b residual = b - Ax d 0 = r 0 search direction for k = 1, 2, 3, . . . x k = x k-1 + … new approx solution r k = new residual d k = new search direction
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Conjugate gradient iteration for Ax = b x 0 = 0 approx solution r 0 = b residual = b - Ax d 0 = r 0 search direction for k = 1, 2, 3, . . . α
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CgIntro - Administrivia Administrivia Homework 4 on web...

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