Numerical Methods & Scientific Computing: lecture notes
Linear Systems
LU factorization
Many software libraries contain no provision for Gauss Elimination — WHY NOT?
if you solve Ax = b1 (⇡ 1 n3 operations) and, some time later, 133
solve Ax = b2 (⇡ 3 n operations) most of these operations have been done before! (all but n2 operations)
=) try to store information so you don’t waste this e↵ort.
In practice, we store the multipliers lij in a lower triangular matrix
l43 1
lij i>j L=:1i=j 0i