
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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PYTHON LU FACTORIZATION

Transcribed Image Text:Program (in a Python function; hint: extend the function from Assignment 1) a
(mxm)
LU factorization algorithm (using complete pivoting) for a square matrix A and
compute the PQLU factors. The factorization is obtained by elimination steps
k-1,...,m-1 so that
A+ A- A v
and j=k,...,m
where the multipliers mik are given by mik =
When km-1, A is upper
triangular, that is, U₁ = A). The lower triangular matrix is obtained using the
multipliers mi, that is Lijmij Vi>j. Li = 1, and Lij=0Vi<j. However, every
k-step selects a pivot A of maximum absolute value via row exchanges recorded in the
permutation matrix P, and column exchanges recorded in the permutation matrix Q.
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