A procedure for decomposing an matrix
into a product of a lower Triangular Matrix
and an upper Triangular Matrix
,

(1) |

(2) |

(3) |

(4) | |

(5) | |

(6) |

(7) |

(8) | |||

(9) |

for , ..., . Then solve for . This can be done by back substitution

(10) | |||

(11) |

for , ..., .

**References**

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``LU Decomposition and Its Applications.''
§2.3 in *Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England:
Cambridge University Press, pp. 34-42, 1992.

© 1996-9

1999-05-25