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).

Notes: