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Unformatted text preview: Homework 3 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesday, 9/22/09 Problem 3.1 Suppose A R n n is a nonsymmetric nonsingular diagonally dominant matrix with the following nonzero pattern (shown for n = 6) * * * * * * * * 0 0 0 0 * * 0 0 0 * 0 0 * 0 0 * 0 0 0 * * 0 0 0 0 * It is known that a diagonally dominant (row or column dominant) matrix has an LU factor- ization and it can be computed stably without pivoting. 3.1.a . Describe an algorithm that solves Ax = b as efficiently as possible. 3.1.b . Given that the number of operations in the algorithm is of the form Cn k + O ( n k- 1 ), where C is a constant independent of n and k > 0, what are C and k ? Problem 3.2 It is known that if partial or complete pivoting is used to compute PA = LU or PAQ = LU of a nonsingular matrix then the elements of L are less than 1 in magnitude, i.e., | ij | 1....
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This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.
- Spring '11