This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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....
View Full Document