Solving Simultaneous Equations Using LU Decomposition

Given a system of linear equations in the formwe can use the LU factorisation ofto solve the linear systemin a two-step triangular process.

Letso thatThe solution is obtained by solving recursively the two systems


Example: Use LU decomposition to solve




we can write the matrix form of the system

The matrix decomposes:

We solve

|From which

Now solve

We have

The original system of equations is

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