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LU decomposition

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LU Solvers

For the system of equations Ax=b.
The solvers based on factorization are widely popular. The factorization of a non singular matrix A in two matrices L and U, called lower and upper matrices, leads to a direct procedure for the evaluation of the inverse of the matrix. Thus making it possible to calculate the solution vector with given source vector. It now remains a two step process: a forward substitution followed by a backward substitution.


Calculate LU factors of A
Ax = (LU)x = L(Ux) = Ly = b
Solve Ly = b by forward substitution
y = L-1b
Solve Ux=y by backward substitution
x = U-1y

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