NMath User's Guide

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Chapter 7. Solutions of Linear Systems (.NET, C#, CSharp, VB, Visual Basic, F#)

NMath provides classes for computing and storing the LU factorization for a matrix.

LU factorization is a procedure for decomposing a matrix into a product of a lower triangular matrix and an upper triangular matrix. Given a matrix A, an LU factorization class factors A as follows:


where P is a permutation matrix, L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.

Once an LU factorization is constructed, it can be reused to solve for different right-hand sides, to compute inverses, to compute condition numbers, and so on.

NMath also provides several static functions for solving linear systems, and for computing determinants, inverses, and condition numbers.