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# Homework02 - U Washington AMATH 352 Winter 2010 Homework 2...

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U. Washington AMATH 352 - Winter 2010 Homework 2 - Due on 01/22/10 The first exercise should be submitted via Scorelator (4 attempts are available). Remember to use the command save with the flag -ascii to output your results. Upload only your “.m” files. 1. (15 points) The goal of the exercise is to program the power method, which is the simplest iterative algorithm to compute the largest eigenpair of a matrix, i.e. the pair ( x , λ ) with the largest value λ R such that Ax = λ x . The algorithm goes as follows Input A , x 0 , and M . for k = 1 to M do, y = Ax k - 1 r k = ( y ) 2 / ( x k - 1 ) 2 x k = y / k y k 2 end do where ( y ) 2 denotes the second component of y . Use the matrix and the initial vector A = 6 5 - 5 2 6 - 2 2 5 - 1 x 0 = - 1 1 1 . Set M = 30 . The vector x 30 is the vector x k with k = 30 , i.e. after 30 steps in the loop. Output the vector x 30 (in x30.dat) and the ratio r 30 (in r30.dat). To validate your code, I recommend that you compute by hand x 1 , r 1 , x 2 , and r 2 and you compare these values with the ones from your code.

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Homework02 - U Washington AMATH 352 Winter 2010 Homework 2...

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