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LU Decomposition, Cont'd
Why is this better?
- Solving triangular matrices is easy: just use forward substitution for (1), backsubstitution for (2).
Problem is, how to decompose A into L and U?
- Expand matrix multiplication LU to get n2 equations for n2 + n unknowns (elements of L and U plus n extras because diagonal elements counted twice).
- Get an extra n equations by choosing Lii = 1 (i = 1,n).
- Then use Crout's algorithm for finding solution to these n2 + n equations "trivially" (NRiC 2.3).