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exam2f10 - Foundations of Computational Math I Exam 2...

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Foundations of Computational Math I Exam 2 Take-home Exam Open Notes, Textbook, Homework Solutions Only Due beginning of Class Wednesday, December 1, 2010 Question Points Points Possible Awarded 1. Iterative Methods 25 for Ax = b 2. Iterative Methods 30 for Ax = b 3. Nonlinear Equations 30 4. Nonlinear Equations 25 Total 110 Points Name: Alias: to be used when posting anonymous grade list. 1
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Problem 1 (25 points) Suppose B R n × n is a symmetric positive definite tridiagonal matrix of the form B = D r L L T D b where n = 2 k , D r and D b are diagonal matrices of order n/ 2, L is a lower triangular matrix with nonzeros restricted to its main diagonal and its first subdiagonal, and U is upper triangular matrix with nonzeros restricted to its main diagonal and its first superdiagonal. Assume that Ax = b can be solved using Jacobi’s method, i.e., the iteration converges acceptably fast. Partition each iterate x i into the top half and bottom half, i.e., x i = x ( top ) i x ( bot ) i 1.a . Assume an initial guess x 0 is given and identify what information, i.e., the pieces
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