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Example
We shall solve the system
Stage l: An LU decomposition of the system is
Stage 2: Set y = U1x and then solve the system L1y = b, i.e.,
Using forward substitution, we obtain:
Stage 3: Solve
Back-substitution now yields:
Thus the solution of Ax = b is:
which may be checked, using the original equations. We turn now to the problem of finding an LU decomposition of a given square matrix A.
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