Crout's Method

A root-finding algorithm used in LU decomposition. It solves the N^2 equations

 i<j    l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ii)u_(ij)=a_(ij)
i=j    l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ii)u_(jj)=a_(ij)
i>j    l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ij)u_(jj)=a_(ij)

for the N^2+N unknowns l_(ij) and u_(ij).

See also

LU Decomposition

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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.

Referenced on Wolfram|Alpha

Crout's Method

Cite this as:

Weisstein, Eric W. "Crout's Method." From MathWorld--A Wolfram Web Resource.

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