LUDecomposition Class

public sealed class LUDecomposition

Public NotInheritable Class LUDecomposition

public ref class LUDecomposition sealed

[<SealedAttribute>]
type LUDecomposition = class end

Inheritance

Object    LUDecomposition

An LU decomposition is a representation of a matrix M as the product of a lower-left-triangular matrix L and and an upper-right-triangular matrix U. To reduce numerical instabilities, we actually decompose a row-wise permutation of a matrix, so that we have P A = L U, where P is a permutation matrix.

For example, here is an LU decomposition of a permutation of a simple 3 X 3 matrix:

Given an LU decomposition of a permutation A, we can solve systems of linear equations or compute the determinant or inverse of A. LU decomposition is the fastest way to solve an arbitrary system of linear equations. It is much faster, and less subject to rounding errors, to solve Ax=b by LU decomposition than than by inverting A and multiplying A^-1b.

You can use the LUDecomposition method to obtain the LU decomposition of any non-singular square matrix.

Reference