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Unformatted text preview: Homework #2 1. (a) Find the PLU factorization of the matrix A =  2 1 1 1 2 1 4 1 2 4 2 using Gaussian elimination with row pivoting. (b) Use these results to compute the determinant of A . (c) Use the PLU factorization and forward and back substitution to solve the linear system of equations A~x = ~ b , with ~ b = [1 , , 1 , 0] t . (d) Use the PLU factorization and forward and back substitution to solve the linear system of equations A~x = ~ b , with ~ b = [0 , 1 , , 1] t . 2. Consider the Babylonian method solving the fixed point problem x = 1 2 x + c x to approximate 2. (a) Perform fixed point iterations with initial guess x = 1 and stop according to the converged stopping condition  x k x k 1  10 4 . (b) Find the relative error of your final approximation. 3. Consider the nonlinear equation x 2 3 = 0 and the naive attempt at a fixed point problem x 2 + x 3 = x obtained by adding x on both sides. Starting with initialon both sides....
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This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff
 Determinant, Gaussian Elimination

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