Chapter-11 - Special Matrices and Gauss-Seidel Chapter 11...

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Unformatted text preview: Special Matrices and Gauss-Seidel Chapter 11 • Certain matrices have particular structures that can be exploited to develop efficient solution schemes. – A banded matrix is a square matrix that has all elements equal to zero, with the exception of a band centered on the main diagonal. These matrices typically occur in solution of differential equations. – The dimensions of a banded system can be quantified by two parameters: the band width BW and half-bandwidth HBW. These two values are related by BW=2HBW+1. • Gauss elimination or conventional LU decomposition methods are inefficient in solving banded equations because pivoting becomes unnecessary. Fig 11.1 Tridiagonal Systems • A tridiagonal system has a bandwidth of 3: = 4 3 2 1 4 3 2 1 4 4 3 3 3 2 2 2 1 1 r r r r x x x x f e g f e g f e g f • An efficient LU decomposition method, called...
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This note was uploaded on 02/15/2010 for the course CHEN 320 taught by Professor Staff during the Spring '08 term at Texas A&M.

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Chapter-11 - Special Matrices and Gauss-Seidel Chapter 11...

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