HW11solution

# HW11solution - Homework 11 Solution 1. For the following...

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Homework 11 Solution 1. For the following matrix: A = 2 4 - 1 3 0 2 1 1 0 (a) [1pt] Using Matlab, ﬁnd Q and R by using the following commend: ‘[Q, R] = qr(A)’. (b) [2pt] For Q and R , perform three iterations of the QR algorithm for ﬁnding eigenvalues of A . You may use a calculator for numerical computations, but show computational steps by hand. (c) [1pt] Compute the eigenvalues of A by using the formula det( A - λ I ) = 0 and compare the result with (b). What is the true percentage relative error in the dominant eigenvalue? You may use a calculator for numerical computations, but show computational steps by hand. Solution: (a) ﬁnd Q and R using Matlab Q = 0 . 5345 0 . 8105 0 . 2394 0 . 8018 - 0 . 5759 0 . 1596 0 . 2673 0 . 1066 - 0 . 9577 , R = 3 . 7417 2 . 4054 1 . 0690 0 3 . 3488 - 1 . 9623 0 0 0 . 0798 (b) Let A 0 = A , Q 0 = Q and R 0 = R Iteration 1: A 1 = R 0 Q 0 = 4 . 2143 1 . 7615 0 . 2560 2 . 1605 - 2 . 1379 2 . 4139 0 . 0213 0 . 0085 - 0 . 0764 Q 1 = 0 . 8899

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## This note was uploaded on 11/14/2011 for the course EAME 250 taught by Professor Lee during the Spring '11 term at Case Western.

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HW11solution - Homework 11 Solution 1. For the following...

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