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hw1 - Due September 4 2008 CS 257(Luke Olson Homework#1...

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Due: September 4, 2008 CS 257 (Luke Olson): Homework #1 Problem 1 Problem 1 [Timing] While developing code for a project, we notice that the implementation of our numerical method strongly depends on the size of the data with which we are working. Suppose we time ( t ) our method with n pieces of data and notice the following timing results (see timing data.m ): n t (milliseconds) 1 4.700000e+00 6 8.770584e+02 11 5.364180e+03 16 1.646625e+04 21 3.718331e+04 26 7.051535e+04 31 1.194624e+05 36 1.870244e+05 41 2.762014e+05 46 3.899935e+05 51 5.314005e+05 56 7.034225e+05 61 9.090595e+05 66 1.151312e+06 71 1.433179e+06 76 1.757661e+06 81 2.127758e+06 86 2.546470e+06 91 3.016797e+06 96 3.541739e+06 Determine the dependence on n (e.g. is the dependence O ( n α )?). Hint: look at plot , semilogy , loglog , in Matlab. Hand in your estimate and justify with either a plot or with a short script . Page 1 of 3
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Due: September 4, 2008 CS 257 (Luke Olson): Homework #1 Problem 2 Problem 2 [Errors] While testing our code further we also notice that the accuracy of our numerical method improves as we use more data (great!). Testing our method with known results and with data size n , we record the following errors in our calculation (see
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