One of the most commonly used applications of the LU decomposition is solving linear equations. It is so often applicable because while the LU decomposition of a system matrix costs O(N ³) operations, solving a system of linear equations with matrix A = LU costs only O(N ²). Therefore, it is possible to perform the LU decomposition of matrix A and then use it to solve systems of equations with different right sides for O(N ²) operations.

Note #1
Algorithm of a matrix condition number estimate can be used to estimate the matrix condition number and any solution errors found.

The module contains two subroutines. The RMatrixLUSolve subroutine solves a system whose LU decomposition has already been performed. The RMatrixSolve subroutine performs the LU decomposition and calls the first subroutine. Use the second subroutine to solve a system of linear equations once. To solve repeated systems with the same left sides, call the RMatrixLU and pass its output to the RMatrixLUSolve subroutine.

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C#

C# 1.0 source.
rsolve.csharp.zip - Solution of the system with general real matrix

C++

C++ source.
rsolve.cpp.zip - Solution of the system with general real matrix
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

C++, multiple precision arithmetic

C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
rsolve.mpfr.zip - Solution of the system with general real matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
rsolve.delphi.zip - Solution of the system with general real matrix

Visual Basic 6

Visual Basic 6 source.
rsolve.vb6.zip - Solution of the system with general real matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
rsolve.zonnon.zip - Solution of the system with general real matrix