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Unformatted text preview: 10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #11: Numerical Calculation of Eigenvalues and Eigenvectors. Singular Value Decomposition (SVD). Singular Value Decomposition (SVD) How do you handle poorly conditioned matrices? A x = b What are corresponding eigenvalues for rectangular matrix? ( ) A A or eigenvalues? eigenvectors? Lots of equations and not many unknowns rectangular matrix [ ] = = = ) ( ) , ( ) ( ) ( ) ( ) ( x c c x f dx x x a x q x f O n n n infinite number of equations, finite number of c n Another scenario: Determine how plant is operating: You make more measurements than unknowns . A T A : eigenvalues : = A A A A T T i i = singular values of A small square matrix A = U V...
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- Fall '04