HW2suggestions - 7 3 7 4 4 2 and vector b = 1 2 3 4 (a)...

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Jacobs University, Bremen School of Engineering and Science Prof. Dr. Lars Linsen, Orif Ibrogimov Spring Term 2010 Homework 2 120202: ESM4A - Numerical Methods Homework Problems 2.1. Let a and b be normalized floating point numbers such that 31 32 a b 1023 1024 . Show that at most 10 and at least 5 significant binary bits are lost in the substraction b - a . ( 10 points ) 2.2. Given matrix A = 3 - 10 - 4 4 - 9 2 - 1 5 4 and vector b = 1 2 3 (a) Compute the LU decomposition of matrix A using Gaussian elimination with scaled partial pivoting. (b) Solve the equation Ax = b for x using the LU decomposition. ( 5+5 points )
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2.3. Given matrix A = 2 1 5 1 3 2 11 1 2 8
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Unformatted text preview: 7 3 7 4 4 2 and vector b = 1 2 3 4 (a) Check whether Gaussian elimination with scaled partial pivoting can be applied to solve the equation Ax = b . (b) Solve the equation Ax = b for x using Gaussian elimination with scaled partial pivoting. ( 5+5 points ) 2.4. (Bonus) Let we are given n × n matrix A such that its all n principal minors are nonsingular. Show that A has an LU-decomposition. ( 10 bonus points ) Due: 17.02.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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HW2suggestions - 7 3 7 4 4 2 and vector b = 1 2 3 4 (a)...

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