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Use of LU decomposition - Tutorial 3

Posted by BMFRGuru at 7:58 PM

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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