LU decomposition

Lower–Upper (LU) decomposition or factorization to solve the set of n linear equations Ax=b.

LU decomposition (factorization) of a nonsingular (square) matrix A means expressing the matrix as the multiplication of a lower triangular matrix L and an upper triangular matrix U, where a lower/upper triangular matrix is a matrix having no nonzero elements above/below the diagonal. For the case where some row switching operation is needed like in the Gauss elimination, we include a permutation matrix P representing the necessary row switching operation(s) to write the LU decomposition as P A = L U.

Reference:

Applied Numerical Methods Using MATLAB®

Author(s): Won Young Yang, Wenwu Cao, Tae‐Sang Chung, John Morris

First published:14 January 2005

Print ISBN:9780471698333 |Online ISBN:9780471705192 |DOI:10.1002/0471705195

Copyright © 2005 John Wiley & Sons, Inc.