linbox

Block Lanczos iteration. More...
#include <blocklanczos.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 >  
Vector &  solve (const Blackbox &A, Vector &x, const Vector &b) 
Solve the linear system Ax = b. More...  
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 to a single vector $v$ during each iteration, the block box is applied to an matrix or, equivalently, to vectors Scalars in the original iteration become 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.

inline 
Constructor.
F  Field over which to operate 
traits  SolverTraits structure describing user options for the solver 

inline 
Constructor with a random iterator.
F  Field over which to operate 
traits  SolverTraits structure describing user options for the solver 
r  Random iterator to use for randomization 
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.
A  Black box for the matrix A 
x  Vector in which to store solution 
b  Righthand side of system 