CholeskyTestProblem

CholeskyTestProblem - 0 0 1 >> U =...

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CEG/MTH/416/616 Winter 2009 Handout Feb 3, 2009 Discussion of L DU and Cholesky for an example real, symmetric, positive definite matrix >> A A = 9 18 -9 -18 18 40 -10 -20 -9 -10 41 82 -18 -20 82 165 >> Lunit Lunit = 1 0 0 0 2 1 0 0 -1 2 1 0 -2 4 2 1 >> D2 D2 = 9 0 0 0 0 4 0 0 0 0 16 0 0 0 0 1 >> Uunit Uunit = 1 2 -1 -2 0 1 2 4 0 0 1 2 0
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Unformatted text preview: 0 0 1 >> U = D2*Uunit 9 18 -9 -18 0 4 8 16 0 0 16 32 0 0 0 1 The L U decomposition is A = Lunit * U The L DU decomposition is A = Lunit * D2 * Uunit Let D = sqrt(D2) The Cholesky factorization is A = LL T Lchol = Lunit*D = (D*Uunit)' >> chol(A) ans = 3 6 -3 -6 0 2 4 8 0 0 4 8 0 0 0 1 >> eig(A) ans = 0.1962 0.3214 43.2406 211.2418...
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