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Unformatted text preview: MAE 107 Computational Methods Summer Session II 2009 Homework # 2 due on Wednesday, August 19 in class 4 problems 20 points Guidelines : Please turn in a neat homework that gives all the formulae that you have used and all the necessary information for the grader to understand your solution. Also, if the problem requires you to write a MATLAB code, please turn in a copy of the code you used, carefully documented with comments and using proper indentation, as well as the requested ouputs and graphs, along with the written explanation of your solution. Problem 1 8 points LU decomposition 1. Create a Matlab function ludec.m that implements the LU decomposition of a square matrix A using Gauss elimination without pivoting as presented in class. Your function should take A as input, and should return an error message (i) if A is not square and (ii) if pivoting is necessary (that is, if one of the pivot elements is equal to zero). The outputs of the function should be two matrices L and U where L is lower triangular with diagonal coefficients equal to 1, and U is an upper triangular matrix. 2. Use this function to compute the LU decomposition of the following matrices: A 1 = 3 9- 1- 3- 11 8 6 24- 24 , A 2 = 4 2 1 2 20 10 4 Check your answers by computing the product L*U of the two matrices obtained (you should find that it is equal to A ). 3. Create a second function linsys_lu that solves the linear system A . x = b using the LU decomposi- tion obtained with Gauss elimination without pivoting. Your function should take as input a square matrix A and a column vector b and return the answer x when it exists. You should compute the LU decomposition of A using the function...
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This note was uploaded on 10/11/2011 for the course MAE 107 taught by Professor Rottman during the Summer '08 term at UCSD.
- Summer '08