Crout's Method

A Root finding technique used in LU Decomposition. It solves the $N^2$ equations

$i<j \qquad l_{i1}u_{1j}+l_{i2}u_{2j}+\ldots+l_{ii}u_{ij}=a_{ij}$
$i=j \qquad l_{i1}u_{1j}+l_{i2}u_{2j}+\ldots+l_{ii}u_{jj}=a_{ij}$
$i>j \qquad l_{i1}u_{1j}+l_{i2}u_{2j}+\ldots+l_{ij}u_{jj}=a_{ij}$

for the $N^2+N$ unknowns $l_{ij}$ and $u_{ij}$.

See also LU Decomposition

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 36-38, 1992.