Introduction to Numerical Analysis I

MATH/CMPSC 455

LU Factorization

LU FACTORIZATION

LU-factorization is a matrix representation of Gaussian elimination

Example:

Example:

Proposition: Let denote the lower triangular matrix whose only nonzero entries are 1’s on the main diagonal and –c in (i,j) position. The it represents the row operation “subtracting c times row j from row i.”

Proposition:

Proposition:

OPERATION COUNT

The LU factorization for a system of n equations in n variables can be completed by operations