lecture11 - CMPSC/MATH 451 Numerical Computations Lecture...

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CMPSC/MATH 451 Numerical Computations Lecture 11 September 16, 2011 Prof. Kamesh Madduri
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Review of last class HW1 discussion 2
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This class Operation count for Gaussian Elimination Studied Octave code: badlufact, lutx Uniqueness of LU factorization Viewing matrices as submatrices Operation count for Inversion Gaussian-Jordan Elimination Covered on blackboard, corresponding slides from textbook follow. 3
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Existence, Uniqueness, and Conditioning Solving Linear Systems Special Types of Linear Systems Software for Linear Systems Triangular Systems Gaussian Elimination Updating Solutions Improving Accuracy Implementation of Gaussian Elimination Gaussian elimination has general form of triple-nested loop for for for a ij = a ij - ( a ik /a kk ) a kj end end end Indices i , j , and k of for loops can be taken in any order, for total of 3! = 6 different arrangements These variations have different memory access patterns, which may cause their performance to vary widely on different computers Michael T. Heath Scientific Computing 60 / 88
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Existence, Uniqueness, and Conditioning Solving Linear Systems Special Types of Linear Systems Software for Linear Systems Triangular Systems Gaussian Elimination Updating Solutions Improving Accuracy Uniqueness of LU Factorization Despite variations in computing it, LU factorization is unique up to diagonal scaling of factors Provided row pivot sequence is same, if we have two LU factorizations PA = LU = ˆ L ˆ U , then ˆ L - 1 L = ˆ UU -
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This note was uploaded on 01/19/2012 for the course CMPSC 451 taught by Professor Staff during the Spring '08 term at Penn State.

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lecture11 - CMPSC/MATH 451 Numerical Computations Lecture...

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