Concept

# Crout matrix decomposition

Summary
In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix. So, if a matrix decomposition of a matrix A is such that: :A = LDU being L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method produces :A = L(DU) and Crout's method produces :A = (LD)U. Implementations C implementation: void crout(double const **A, double **L, double **U, int n) { int i, j, k; double sum = 0;
``````for (i = 0; i < n; i++) {
U[i][i] = 1;
}

for (j = 0; j < n;
``````
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