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Unformatted text preview: Homework 6 Math 471, Fall 2007 Assigned: Friday, October 19, 2006 Due: Friday, October 26, 2006 • Include a cover page • Clearly label all plots using title , xlabel , ylabel , legend • Use the subplot command to compare multiple plots • Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Condition Numbers, P. 187 #1, 2) 1. Let A and B be n × n matrices, and α be a nonzero real number. (a) Show that κ ( AB ) ≤ κ ( A ) κ ( B ); (b) Show that κ ( αA ) = κ ( A ). 2. Let A be an n × n matrix, and suppose that A x = y for some vectors x and y . Show that κ ( A ) ≥ k A kk x k k y k . (2) (Error Estimates, P. 188 #7c, 8c) 7c. Compute κ ∞ for A = 1 1 1 1 1 1 8c. Compute the error e = ˜ x x and the residual r = A ˜ x b and then compare the relative error to the condition number times the relative residual with l ∞ norm....
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 Winter '08
 LinZhi
 Math, Numerical Analysis, Cholesky Decomposition, Matrices, ax, Hilbert matrix Hn

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