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hw3ceg416wi10

# hw3ceg416wi10 - For the B matrix of Problem 1 and the right...

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Page 1 of 1 1/26/2010 CEG/MTH/416/616 Spring 2009 CEG/MTH/416/616 Matrix Computations Homework Set # 3 30 points max undergraduate 40 points max graduate Assigned January 26, 2010. Due February 2, 2010 Problem 1 (10 points) Study the Sherman-Morrison Formula (Datta, First Edition, page 239). (a) (5 points) Prove the identity. (b) (5 points) Use to find the inverse of the 3 by 3 matrix A = H uv T where H=hilb(3) and u=[3;2;1] and v=[1;1;1]. Use the MATLAB hilb and invhilb commands. Note H -1 is >> B = invhilb(3) ans = 9 -36 30 -36 192 -180 30 -180 180 Problem 2 (20 points)
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Unformatted text preview: For the B matrix of Problem 1 and the right hand side vector, c = [1;1;1], solve B*y=c using the methods below. Which method is "best"? Which method is "easy"? (a) (5 points) Gaussian elimination with partial (row) pivoting. (b) (5 points) Gaussian elimination with full (row & column) pivoting. (c) (5 points) Gaussian elimination with row scaling. (d) (5 points) Iterative refinement starting with y=B\c. How many iterations are necessary? Problem 3 (10 points – Graduate Students only) Datta First edition, problem 23 part (a) page 302....
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