linbox
Public Member Functions
BlockLanczosSolver< Field, Matrix > Class Template Reference

Block Lanczos iteration. More...

#include <block-lanczos.h>

Public Member Functions

 BlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits)
 Constructor. More...
 
 BlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits, typename Field::RandIter r)
 Constructor with a random iterator. More...
 
template<class Blackbox , class Vector >
Vectorsolve (const Blackbox &A, Vector &x, const Vector &b)
 Solve the linear system Ax = b. More...
 

Detailed Description

template<class Field, class Matrix = BlasMatrix<typename Field::Element>>
class LinBox::BlockLanczosSolver< Field, Matrix >

Block Lanczos iteration.

This is a blocked version of the iteration given in LanczosSolver. The essential difference is that, rather than applying the black box $A$ to a single vector $v$ during each iteration, the block box $A$ is applied to an $n\times N$ matrix $V$ or, equivalently, to $N$ vectors $v_1, \ldots, v_N$ Scalars in the original iteration become $N\times N$ matrices in the blocked version. The resulting iteration is a natural extension of the basic theory of the original Lanczos iteration, c.f. (see Montgomery 1995 ). This has the advantage of more flexible parallelization, and does not break down as often when used over small fields.

Currently, only dense vectors are supported for this iteration, and it is unlikely any other vector archetypes will be supported in the future.

Bibliography:
[Montgomery '95]

Constructor & Destructor Documentation

BlockLanczosSolver ( const Field &  F,
const BlockLanczosTraits &  traits 
)
inline

Constructor.

Parameters
FField over which to operate
traitsSolverTraits structure describing user options for the solver
BlockLanczosSolver ( const Field &  F,
const BlockLanczosTraits &  traits,
typename Field::RandIter  r 
)
inline

Constructor with a random iterator.

Parameters
FField over which to operate
traitsSolverTraits structure describing user options for the solver
rRandom iterator to use for randomization

Member Function Documentation

Vector & solve ( const Blackbox &  A,
Vector x,
const Vector b 
)

Solve the linear system Ax = b.

If the system is nonsingular, this method computes the unique solution to the system Ax = b. If the system is singular, it computes a random solution.

If the matrix A is nonsymmetric, this method preconditions the matrix A with the preconditioner D_1 A^T D_2 A D_1, where D_1 and D_2 are random nonsingular diagonal matrices. If the matrix A is symmetric, this method preconditions the system with A D, where D is a random diagonal matrix.

Parameters
ABlack box for the matrix A
xVector in which to store solution
bRight-hand side of system
Returns
Reference to solution vector

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