1. Introduction to Numerical Analysis I MATH/CMPSC 455 LU Factorization

2. LU F ACTORIZATION LU-factorization is a matrix representation of Gaussian elimination

3. Example:

4. 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:

5. O PERATION C OUNT The LU factorization for a system of n equations in n variables can be completed by operations