Test your code on randomly generated problems of

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Unformatted text preview: ) (b) Now assume that k ≪ n. Describe an efficient method to solve the normal equations found in part (a). Give an approximate flop count for a general method that does not exploit structure, and also for your efficient method. (c) A numerical instance. In this part you will try out your efficient method. We’ll choose k = 100 and n = 4000, and δ = η = 1. First, randomly generate A and b with these dimensions. Form the normal equations as in part (a), and solve them using a generic method. Next, write (short) code implementing your efficient method, and run it on your problem instance. Verify that the solutions found by the two methods are nearly the same, and also that your efficient method is much faster than the generic one. 75 Note: You’ll need to know some things about Matlab to be sure you get the speedup from the efficient method. Your method should involve solving linear equations with tridiagonal coefficient matrix. In this case, both the factorization and the back substitution can be carried out very efficiently. The Matlab documentation says that banded matrices are recognized and exploited, when solving equations, but we found this wasn’t always the case....
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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