# h2 - CS 510 Homework due I Using Gaussian elimination with...

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CS 510 Homework - due 10/12/10 I. Using Gaussian elimination with partial pivoting ,obta ina PA = LU decomposition of A = 1 - 1 - 2 2 - 2 - 1 102 and use it to solve Ax = 1 5 4 . [You can check your results using matlab command A \ b and ’lu’ .] II. Obtain a Cholesky ( ˜ L ˜ L T ) factorization of A = 4 - 2 - 25 - 2 - 4 452 28 . [You can check your answer using matlab function ’chol’ .] III. Assume A is a nonsingular n × n matrix. .. (i) Suppose A - 1 is computed by applying Gaussian elimination to A , then using the resulting LU decomposition to solve Ax ( k ) = e ( k ) ,k =1 , ..., n . How many operations will this take: (a) if the zero structure of the e ( k ) ’s is not taken into account, (b) if the zero structure of the e ( k ) ’s is taken into account. (ii) Suppose C = A - 1 B is to be computed, where B is n × n . How many operations will this take (a) if this is done by ﬁrst computing A - 1 , then postmultiplying by B ,(b )i f the columns c j = A - 1 b j of C ( b j =co lumn j of B ) are computed by solving Ac j = b j , j , ..., n .

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## This note was uploaded on 10/06/2010 for the course CS CS 510 taught by Professor Richter during the Fall '10 term at Rutgers.

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h2 - CS 510 Homework due I Using Gaussian elimination with...

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