triangular

triangular - EE103 (Fall 2009-10) 4. Triangular matrices...

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Unformatted text preview: EE103 (Fall 2009-10) 4. Triangular matrices terminology forward and backward substitution inverse 4-1 Definitions a square matrix A is lower triangular if a ij = 0 for j > i A = a 11 a 21 a 22 . . . . . . . . . a n- 1 , 1 a n- 1 , 2 a n- 1 ,n- 1 a n 1 a n 2 a n,n- 1 a nn A is upper triangular if a ij = 0 for j < i ( A T is lower triangular) a triangular matrix is unit upper/lower triangular if a ii = 1 for all i a triangular matrix is nonsingular if the diagonal elements are nonzero Triangular matrices 4-2 Forward substitution solve Ax = b with A lower triangular and nonsingular a 11 a 21 a 22 . . . . . . . . . . . . a n 1 a n 2 a nn x 1 x 2 . . . x n = b 1 b 2 . . . b n Algorithm : x 1 := b 1 /a 11 x 2 := ( b 2 a 21 x 1 ) /a 22 x 3 := ( b 3 a 31 x 1 a 32 x 2 ) /a 33 ....
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This note was uploaded on 10/15/2009 for the course EE 103 taught by Professor Vandenberghe,lieven during the Spring '08 term at UCLA.

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triangular - EE103 (Fall 2009-10) 4. Triangular matrices...

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