template<class Field, class Matrix = BlasMatrix<Field,typename RawVector<typename Field::Element >::Dense>>
class LinBox::MGBlockLanczosSolver< 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 during each iteration, the block box is applied to an matrix or, equivalently, to $N$ 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. (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.
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.