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hw5_part2_solutions

# hw5_part2_solutions - Cholesky factorization U = 2.8284...

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Problem 4 MATLAB Command Window EDU>> HW5_Prob4 permutation matrix such that P*A=L*U 0 1 1 0 lower triangular matrix, L 1 0 0 1 upper triangular matrix, U 1 1 0 1 MATLAB m-file HW5_Prob4.m A = [0 1; 1 1]; [L,U,P] = lu(A) ; disp(' '); disp(' '); disp('permutation matrix such that P*A=L*U') disp(P); disp('lower triangular matrix, L') disp(L); disp('upper triangular matrix, U') disp(U); Note: In this case, we cannot use [L, U] = lu(A) to get a lower triangular matrix and an upper triangular matrix. The command [L, U] = lu(A) gives the result: L = [ 0 1 ; 1 0 ] U = [ 1 1 ; 0 1 ] Although A = L*U, the L matrix obtained above is NOT a lower triangular matrix (L should have nonzero diagonal elements as defined in the textbook).