#include <la-block-lanczos.h>
This is a biorthogonalising variant of Montgomery's block Lanczos iteration. The goal is to avoid having to symmetrise the input matrix by constructing two sequences of block vectors that have mutual orthogonality properties. This algorithm was proposed by Bradford Hovinen.
Public Member Functions | |
LABlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits) | |
LABlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits, typename Field::RandIter r) | |
~LABlockLanczosSolver () | |
template<class Blackbox, class Vector> bool | solve (const Blackbox &A, Vector &x, const Vector &b) |
template<class Blackbox, class Matrix1> unsigned int | sampleNullspace (const Blackbox &A, Matrix1 &x) |
template<class Blackbox> unsigned int | rank (const Blackbox &A) |
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Constructor
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Constructor with a random iterator
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Destructor |
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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.
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Sample uniformly from the (right) nullspace of A
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Estimate the rank of A
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