Let A = 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 , b = 5.00 1.02 1.04 1.10 An approximate
Chapter 7, Problem 38(choose chapter or problem)
Let A = 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 , b = 5.00 1.02 1.04 1.10 An approximate solution of Ax = b is calculated by rounding the entries of b to the nearest integer and then solving the rounded system with integer arithmetic. The calculated solution is x_ = (12, 4, 2, 1)T . Let r denote the residual vector. (a) Determine the values of _r_ and cond(A). (b) Use your answer to part (a) to find an upper bound for the relative error in the solution. (c) Compute the exact solution x and determine the relative error _x x__ _x_ . 3
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