3114p1 - MAS 3114 Section 2481 Extra Credit MATLAB Project...

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Unformatted text preview: MAS 3114 Section 2481 Extra Credit MATLAB Project Due date: May 3, 7:30 AM (bring it to the final exam with you). The problems should be done in a single MATLAB session and saved using the matlab diary function; the saved file should then be printed out and handed in. This project will make use of two facts which were discussed in the lectures, but which do not (unfortunately) appear in the text. The first is the so-called Gerschgorin Circle Theorem: If A = ( a ij ) is an n × n matrix, then the eigenvalues of A are contained in the union of the closed disks | z- a ii | ≤ X i 6 = j | a ij | i = 1 ,...,n. The second is the following theorem: the eigenvalues of a real symmetric matrix are real. 1. Construct a random 5 × 5 matrix B (use the MATLAB rand function), then set A = B T B to get a symmetric matrix (whose eigenvalues are thus real). Use the direct power method ( § 5.8 of the text) to find the largest eigenvalue of A ....
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