Differential Equations Solutions 22

Differential Equations Solutions 22 - (e) Determine whether...

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32 Chapter 5. Solutions: Matrix Factorizations CHALLENGE 5.22. (Partial Solution) (a) Find the null space of a matrix: QR (fast; relatively stable) or SVD (slower but more reliable) (b) Solve a least squares problem: QR when the matrix is well conditioned. Don’t try QR if the matrix is not well-conditioned; use the SVD method. (c) Determine the rank of a matrix: RR-QR (fast, relatively stable); SVD (slower but more reliable). (d) Find the determinant of a matrix: LU with pivoting.
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Unformatted text preview: (e) Determine whether a symmetric matrix is positive denite: Cholesky or eigen-decomposition (slower but more reliable) The LL T version of Cholesky breaks down if the matrix has a negative eigenvalue by taking the square root of a negative num-ber, so it is a good diagnostic. If the matrix is singular, (positive semi-denite), then we get a 0 on the main diagonal, but with rounding error, this is impossible to detect....
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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