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Unformatted text preview: Final Exam II COT 4501 Numerical Analysis This is one of the two final exams for COT4501. You are allowed to attempt both exams, and the better-scored exam will be counted as your final exam. The goal of this exam is to provide you with an opportunity to convincingly demonstrate your mastery of the subject. Unless you experience an (unprecedented) epiphany, this exam will most likely take you more than a few hours to complete. Therefore, you should take your time to read each problem carefully and understand it correctly before valiantly attempting its solution. You can solve the problems using any method you like (including those not covered in class), and in particular, an imaginative but incomplete solution will be valued almost as much as a correct solution. While each problem requires some MATLAB implementation, it is posed as such that it is not necessary to hand in or show your MATLAB code. Finally, you should present your solutions in a brief but lucid write-up. Rules: A. This exam should be an individual effort and you are not permitted to consult with anyone except the instructor (or TA). B. If you need hints for the problems, contact the instructor. C. You are allowed to consult the textbook. D. You are also allowed to consult the Wikipedia pages. No other online sources are permitted. E. Your write-up should be emailed to the instructor before 9:30 am on Monday, May 2, 2011. 1 Problem 1 Singular Value Decomposition (SVD) For this problem, you need to download the data matrix from http://www.cise.ufl.edu/class/cot4501sp11/Final2.html . The given mat-file contains one single 30 × 322 matrix, D . Each row of D gives a collection of 322 points on the line R 1 . These 30 collections of 322 points may look random to you. However, these 1-D points are generated as follows. We start with a collection of 322 2-D points, p 1 , ··· ,p 322 , and for each row i of D , we take a unit 2-D vector u i and project the 2-D points down to the line spanned by u i . That is, D ij = u > i p j , i = 1 , ··· , 30 , j = 1 , ··· , 322 , where D ij...
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- Spring '08
- Linear Algebra, Markov chain, probability distribution vector