Lecture15 - ngineering Analysis ENG 3420 Fall 2009 Dan C....

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Unformatted text preview: ngineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00 2 Lecture 15 Lecture 15 Last time: Discussion of pivoting Tri-diagonal system solver Examples Today: Symmetric matrices; Hermitian matrices. Matrix multiplication Non-commutative Associative The transpose of a product of two matrices LU Factorization (Chapter 10) Cholesky decomposition Next Time Midterm LU Factorization LU factorization involves two steps: Decompose the [ A ] matrix into a product of: a lower triangular matrix [ L ] with 1 for each entry on the diagonal. and an upper triangular matrix [ U Substitution to solve for { x } Gauss elimination can be implemented using LU factorization The forward-elimination step of Gauss elimination comprises the bulk of the computational effort. LU factorization methods separate the time-consuming elimination of the matrix [ A ] from the manipulations of the right-hand-side [ b ]. Gauss Elimination as...
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This note was uploaded on 02/17/2012 for the course EGN 3420 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Lecture15 - ngineering Analysis ENG 3420 Fall 2009 Dan C....

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