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# HW3suggestions - x 1 x 2 x 3 ï£ ï£¸ and b = ï£ ï£­ 1-8 2 5...

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Jacobs University, Bremen School of Engineering and Science Prof. Dr. Lars Linsen, Orif Ibrogimov Spring Term 2010 Homework 3 120202: ESM4A - Numerical Methods Homework Problems 3.1. (a) Prove that the matrix A = 0 1 1 1 does not have an LU - factorization. (b) Find necessary and sufficient condition on a, b, c in order that the matrix a b b c has a factorization LL T in which L is lower triangular. (c) Find the Cholesky factorization of the matrix A = 30 10 5 10 5 3 20 15 12 ( ?+?+? points ) 3.2. Apply the Gauss-Seidel iteration starting with x (0) = (0 , 0 , 0) T to the system Ax = b , where A = 4 - 2 0 2 12 - 4 2 - 1 . 5 4 , x = x 1 x 2
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Unformatted text preview: x 1 x 2 x 3 ï£¶ ï£¸ and b = ï£« ï£­ 1-8 2 . 5 ï£¶ ï£¸ ( 10 points ) 3.3. Let A be a strictly diagonal dominant matrix, i.e. | a ii | > X i 6 = j | a ij | for all rows i . (a) Prove that the Jacobi iteration for solving the linear equation system Ax = b converge for any starting point. (Bonus) Prove that the Gauss-Seidel iteration for solving the linear equation system Ax = b converge for any starting point. ( ?+? points ) Due: 17.02.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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• Spring '10
• xxxxxxxxxyyyyyy
• Elementary algebra, Necessary and sufficient condition, Iterative method, Prof. Dr. Lars Linsen, Dr. Lars Linsen

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