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Slides_2010_02_24 - Applied linear algebra and numerical...

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Applied linear algebra and numerical analysis Session 21 Prof. Ulrich Hetmaniuk Department of Applied Mathematics February 25, 2010
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Office Hours Today ! Office Hours from MGH are moved to ICL Lab from 6:30-8pm. Two new times in GUG 416 (Laptop only) Tuesday 5-8pm Wednesday 5-8pm
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LU Factorization Definition A matrix A is regular if and only if it can be factored A = LU where L is lower-triangular with diagonal entries equal to 1 and U is a upper-triangular matrix with nonzero diagonal entries. The matrix A is invertible.
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Review: Elementary Matrix Operations 1 0 0 a 1 0 b 0 1 2 3 4 5 6 7 8 9 10 = 2 3 4 5 + 2 a 6 + 3 a 7 + 4 a 8 + 2 b 9 + 3 b 10 + 4 b (1) 1 0 0 0 1 0 0 c 1 2 3 4 5 6 7 8 9 10 = 2 3 4 5 6 7 8 + 5 c 9 + 6 c 10 + 7 c (2)
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Review: Elementary Matrix Operations 1 0 0 a 1 0 b 0 1 1 0 0 0 1 0 0 c 1 = 1 0 0 a 1 0 b c 1 1 0 0 0 1 0 0 c 1 1 0 0 a 1 0 b 0 1 = 1 0 0 a 1 0 ac + b c 1
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