OptiVec: MF_CholeskyLimprove

MF_CholeskyLimprove

MD_CholeskyLimprove

ME_CholeskyLimprove

MF_CholeskyRimprove

MD_CholeskyRimprove

ME_CholeskyRimprove

Function

iterative improvement of the solution of a linear system solved by the sequence of Cholesky L/R decomposition and Cholesky L/R solution

Syntax C/C++	#include <MFstd.h> void MF_CholeskyLimprove( fVector X, fVector B, fMatrix MA, fMatrix ML, ui len ); void MF_CholeskyRimprove( fVector X, fVector B, fMatrix MA, fMatrix MR, ui len );
C++ MatObj	#include <OptiVec.h> void vector<T>::CholeskyLimprove( const vector<T> B, const matrix<T>& MA, const matrix<T>& ML ); void vector<T>::CholeskyRimprove( const vector<T> B, const matrix<T>& MA, const matrix<T>& MR );
Pascal/Delphi	uses MFstd; procedure MF_CholeskyLimprove( X, B:fVector; MA, ML:fMatrix; len:UIntSize ); procedure MFb_CholeskyRimprove( X, B:fVector; MA, MR:fMatrix; len:UIntSize );

Description

Especially for large matrices, accumulated round-off error in the solution of a linear system of equations may become quite noticable. This round-off error will translate into inaccurate results of MF_CholeskyLsolve. If the input matrix was not overwritten by the output matrix in the initial call to MF_CholeskyLdecompose, you may call MF_CholeskyLimprove after MF_CholeskyLsolve to improve the accuracy by iteration. MF_CholeskyLimprove needs the output vector X of MF_CholeskyLsolve, the right-hand-side vector B of the linear system, and both the original matrix MA and its raw ML-decomposed form ML as arguments. Likewise, MF_CholeskyRimprove improves a solution obtained with the MR form.