linbox
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Block Lanczos iteration. More...
#include <block-lanczos.h>
Public Member Functions | |
BlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits) | |
BlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits, typename Field::RandIter r) | |
template<class Blackbox , class Vector > | |
Vector & | solve (const Blackbox &A, Vector &x, const Vector &b) |
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 $n N$ matrix $V$ or, equivalently, to $N$ vectors $v_1, , v_N$ Scalars in the original iteration become $N N$ matrices in the blocked version. The resulting iteration is a natural extension of the basic theory of the original Lanczos iteration, c.f. (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.
BlockLanczosSolver | ( | const Field & | F, |
const BlockLanczosTraits & | traits | ||
) | [inline] |
Constructor
F | Field over which to operate |
traits | SolverTraits} structure describing user options for the solver |
BlockLanczosSolver | ( | const Field & | F, |
const BlockLanczosTraits & | traits, | ||
typename Field::RandIter | r | ||
) | [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 |
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.
A | Black box for the matrix A |
x | Vector in which to store solution |
b | Right-hand side of system |