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# Homework04 - U Washington AMATH 352 Winter 2010 Homework 4...

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U. Washington AMATH 352 - Winter 2010 Homework 4 - Due on 02/19/09 The first two exercises should be submitted via Scorelator (4 attempts per exercise are available). Remember to use the command save with the flag -ascii to output your results. Upload only your “.m” files. You will upload, at least, one file per exercise. 1. (10 points) The goal of this exercise is to implement the QR algorithm. Set A and ε . while max i 6 = j | a ij | > ε max i | a ii | , Compute the QR factorization of A . Overwrite A with the product RQ . end while Use the matrix A = 2 - 1 - 3 - 1 6 5 - 3 5 8 and ε = 10 - 12 . Count the number of iterations. Output the resulting diagonal in diagA.dat and the number of iterations in iter.dat. 2. (10 points) Consider the norm k A k = m X i =1 n X j =1 | a ij | where the matrix A = ( a ij ) m × n has m rows and n columns. Write a Matlab code computing this norm. Use the matrix A = 6 5 - 5 2 6 - 2 2 5 - 1 and the matrix B R 123 × 99 generated by Matlab with the random function after resetting the random generator to state 1 (check the previous homeworks). Output, in ASCII format,

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