template<typename _MatrixType, typename _Preconditioner>
class Eigen::DGMRES< _MatrixType, _Preconditioner >

A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse linear systems. The basis is built with modified Gram-Schmidt. At each restart, a few approximated eigenvectors corresponding to the smallest eigenvalues are used to build a preconditioner for the next cycle. This preconditioner for deflation can be combined with any other preconditioner, the IncompleteLUT for instance. The preconditioner is applied at right of the matrix and the combination is multiplicative.

Template Parameters

_MatrixType	the type of the sparse matrix A, can be a dense or a sparse matrix.
_Preconditioner	the type of the preconditioner. Default is DiagonalPreconditioner Typical usage : SparseMatrix<double> A; VectorXd x, b; //Fill A and b ... DGMRES<SparseMatrix<double> > solver; solver.set_restart(30); // Set restarting value solver.setEigenv(1); // Set the number of eigenvalues to deflate solver.compute(A); x = solver.solve(b);

DGMRES can also be used in a matrix-free context, see the following example .

References : [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, https://doi.org/10.1016/j.compfluid.2012.03.023
[2] K. Burrage and J. Erhel, On the performance of various adaptive preconditioned GMRES strategies, 5(1998), 101-121. [3] J. Erhel, K. Burrage and B. Pohl, Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318.