Please, help us to better know about our user community by answering the following short survey: https://forms.gle/wpyrxWi18ox9Z5ae9 Eigen-unsupported  3.3.7 Eigen::GMRES< _MatrixType, _Preconditioner > Class Template Reference

## Detailed Description

### template<typename _MatrixType, typename _Preconditioner> class Eigen::GMRES< _MatrixType, _Preconditioner >

A GMRES solver for sparse square problems.

This class allows to solve for A.x = b sparse linear problems using a generalized minimal residual method. The vectors x and b can be either dense or sparse.

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

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

This class can be used as the direct solver classes. Here is a typical usage example:

int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
// fill A and b
GMRES<SparseMatrix<double> > solver(A);
x = solver.solve(b);
std::cout << "#iterations: " << solver.iterations() << std::endl;
std::cout << "estimated error: " << solver.error() << std::endl;
// update b, and solve again
x = solver.solve(b);

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.

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

class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

## Public Member Functions

Index get_restart ()

GMRES ()

template<typename MatrixDerived >
GMRES (const EigenBase< MatrixDerived > &A)

void set_restart (const Index restart)

## ◆ GMRES() [1/2]

template<typename _MatrixType , typename _Preconditioner >
 Eigen::GMRES< _MatrixType, _Preconditioner >::GMRES ( )
inline

Default constructor.

## ◆ GMRES() [2/2]

template<typename _MatrixType , typename _Preconditioner >
template<typename MatrixDerived >
 Eigen::GMRES< _MatrixType, _Preconditioner >::GMRES ( const EigenBase< MatrixDerived > & A )
inlineexplicit

Initialize the solver with matrix A for further `Ax=b` solving.

This constructor is a shortcut for the default constructor followed by a call to compute().

Warning
this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

## ◆ get_restart()

template<typename _MatrixType , typename _Preconditioner >
 Index Eigen::GMRES< _MatrixType, _Preconditioner >::get_restart ( )
inline

Get the number of iterations after that a restart is performed.

## ◆ set_restart()

template<typename _MatrixType , typename _Preconditioner >
 void Eigen::GMRES< _MatrixType, _Preconditioner >::set_restart ( const Index restart )
inline

Set the number of iterations after that a restart is performed.

Parameters
 restart number of iterations for a restarti, default is 30.

The documentation for this class was generated from the following file: