CME302 Homework 2September 30, 2009T&B 6.1, 6.4, 6.5, 7.1(1)Convince yourself that the algorithms 7.1 and 8.1 are indeed equivalent(here, you do not have to convince us that you’re convinced).Show that theyare equivalent for a 3x3 matrix of your choice.(2)Load ’cameraman.tif’ and view it inMatlabas follows:A = double(imread(’cameraman.tif’));imagesc(A); colormap(gray); axis image;(a)Describe how to construct the rank-kapproximationBktoA. Show us yourcode. (You can do this in two lines ofMatlabcode.)Feel free to downloadmon1.mfrom the Materials section of Coursework tocompare your solution with the one displayed bymon1.m.(The code to formthe approximation is of course inmon1.m, but don’t look at it unless you aredesperate: that would take away the fun.)(b)Let us define the relative error to bee=bardblA−BkbardblFbardblAbardblF.What rank doesBkhave to have to give a relative error of 10%? 1%? (Do thisinMatlab.)(3)
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