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GMRES< _MatrixType, _Preconditioner > Class Template Reference

A GMRES solver for sparse square problems. More...

Inherits IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >.

List of all members.

Public Member Functions

int get_restart ()
 GMRES (const MatrixType &A)
 GMRES ()
void set_restart (const int restart)
template<typename Rhs , typename Guess >
const
internal::solve_retval_with_guess
< GMRES, Rhs, Guess > 
solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

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.

See also:
class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Constructor & Destructor Documentation

GMRES (  )  [inline]

Default constructor.

GMRES ( const MatrixType &  A  )  [inline]

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.

Member Function Documentation

int get_restart (  )  [inline]

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

void set_restart ( const int  restart  )  [inline]

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

Parameters:
restart number of iterations for a restarti, default is 30.
const internal::solve_retval_with_guess<GMRES, Rhs, Guess> solveWithGuess ( const MatrixBase< Rhs > &  b,
const Guess &  x0 
) const [inline]
Returns:
the solution x of $ A x = b $ using the current decomposition of A x0 as an initial solution.
See also:
compute()

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