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Unformatted text preview: ACS I Linear Algebra Homework # 2 Due: Thursday, January 27 1. Suppose A is a symmetric, positive definite tridiagonal matrix given by A = a 1 b 1 ··· ··· ··· b 1 a 2 b 2 ··· ··· b 2 a 3 b 3 ··· . . . . . . . . . . . . . . . . . . . . . . . . ··· ··· b n − 2 a n − 1 b n − 1 ··· ··· ··· b n − 1 a n a. Derive the equations for obtaining a Cholesky factorization of this tridiagonal matrix, taking advantage of the structure and then write pseudo code for the algorithm. b. Determine the equations for solving the linear system Avectorx = vector b once we have the fac- torization A = LL T ; i.e., write the equations for the forward and back solves. Then write pseudo code for your algorithms. c. Determine the operation count for the factorization and the forward and back solves....
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This note was uploaded on 01/15/2012 for the course ISC 5315 taught by Professor Staff during the Spring '11 term at FSU.
- Spring '11