hw6 - CME302 Homework 6(1 Problem 28.2(a(b(c(2 This problem...

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Unformatted text preview: CME302 Homework 6 (1) Problem 28.2 (a) (b) (c) (2) This problem is based on Problem 29.1 from Trefethen. We would like you to put together a MATLAB program that finds all the eigenvalues of a real symmetric matrix, using only elementary building blocks. Use A = hilb (4) to test first four parts of the problem and show the test results on your homework. (a) Write a function T = tridiag ( A ) that reduces a real symmetric m × m matrix to tridiagonal form by orthogonal similarity transformations. Your program should use elementary MATLAB operations only. Add a line that forces T at the end to be exactly symmetric and tridiagonal. (b) Write a function Tnew = qralg ( A ) that runs the unshifted QR algo- rithm on a real tridiagonal matrix T . For the QR factorization at each step, use the programs from Exercise 10.2, or, a new code based on Givens rotations or 2 × 2 Householder reflections rather than m × m operations. Again, enforce symmetry and tridiagonality at each step. Your program should stop and returnsymmetry and tridiagonality at each step....
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