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NA_ex2

# NA_ex2 - 6 2 5 1 A and ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜...

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Assignment 2 Submit Thursday, February 18, 2010 Circle your final answers 1. By using SVD find all solutions of = 79 49 19 9 8 7 6 5 4 3 2 1 3 2 1 x x x Solve the problem by a second method. 2. Find all solutions of = 1250 918 586 254 113 83 53 23 83 61 39 17 53 39 25 11 23 17 11 5 4 3 2 1 x x x x 3. Find a vector x , which minimizes b A x where = 8 4 7 3
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Unformatted text preview: 6 2 5 1 A and ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = 1 4 9 16 b by using (a) SVD (b) Compact QR decomposition (solve (b) by hand) (c) Normal equations in conjunction with LU factorization (solve (c) by hand) 4. Find the symmetric square root of ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = 194 122 50 122 77 32 50 32 14 A , i.e. if A B = then T B B = and BB A = . (Hint: SVD may be a useful tool)....
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• Summer '11
• Staff
• Prime number, Singular value decomposition, Orthogonal matrix, Linear least squares, Matrix decomposition, Compact QR decomposition

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