Switch to control algorithm for linear system solving. More...

#include <flags.h>

Public Types
enum	{ automatic, gauss, divfree, bareiss }

Detailed Description

Switch to control algorithm for linear system solving.

Definition at line 140 of file flags.h.

Member Enumeration Documentation

anonymous enum

Enumerator:

automatic	Let the system choose. A heuristics is applied for automatic determination of a suitable algorithm.
gauss	Gauss elimination. If $m_{i,j}^{(0)}$ are the entries of the original matrix, then the matrix is transformed into triangular form by applying the rules $m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}$ This algorithm is well-suited for numerical matrices but generally suffers from the expensive division (and computation of GCDs) at each step.
divfree	Division-free elimination. This is a modification of Gauss elimination where the division by the pivot element is not carried out. If $m_{i,j}^{(0)}$ are the entries of the original matrix, then the matrix is transformed into triangular form by applying the rules $m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}$ This algorithm is only there for the purpose of cross-checks. It suffers from exponential intermediate expression swell. Use it only for small systems.
bareiss	Bareiss fraction-free elimination. This is a modification of Gauss elimination where the division by the pivot element is delayed until it can be carried out without computing GCDs. If $m_{i,j}^{(0)}$ are the entries of the original matrix, then the matrix is transformed into triangular form by applying the rules $m_{i,j}^{(k+1)} = (m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}) / m_{k-1,k-1}^{(k-1)}$ (We have set $m_{-1,-1}^{(-1)}=1$ in order to avoid a case distinction in above formula.) It can be shown that nothing more than polynomial long division is needed for carrying out the division. This is generally the fastest algorithm for solving linear systems. In contrast to division-free elimination it only has a linear expression swell. For two-dimensional systems, the two algorithms are equivalent, however.

Definition at line 142 of file flags.h.

The documentation for this class was generated from the following file:

flags.h

Public Types

Detailed Description

Member Enumeration Documentation