GMRESR solver for Ax=b. More...

#include <cmath>
#include <vector>
#include "oops/util/dot_product.h"
#include "oops/util/formats.h"
#include "oops/util/Logger.h"

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Namespaces
	oops
	The namespace for the main oops code.

Functions
template<typename VECTOR , typename AMATRIX , typename PMATRIX >
double	oops::GMRESR (VECTOR &xx, const VECTOR &bb, const AMATRIX &A, const PMATRIX &precond, const int maxiter, const double tolerance)

Detailed Description

GMRESR solver for Ax=b.

GMRESR solver for Ax=b. (H.A. Van der Vorst and C. Vuik, 1994, Numerical Linear Algebra with Applications, 1(4), 369-386.) A must be square, but need not be symmetric. (For a symmetric matrix, and constant preconditioner, GMRESR is simply PCG with full orthogonalisation.) A preconditioner must be supplied that, given a vector q, returns an approximate solution of Ap=q. The preconditioner can be variable.

On entry:

x = starting point, \( X_0 \).
b = right hand side.
A = \( A \).
precond = preconditioner \( F_k \approx (A)^{-1} \).

On exit, x will contain the solution. The return value is the achieved reduction in residual norm.

Iteration will stop if the maximum iteration limit "maxiter" is reached or if the residual norm reduces by a factor of "tolerance".

VECTOR must implement:

dot_product
operator(=)
operator(+=),
operator(-=)
operator(*=) [double * VECTOR],
axpy

AMATRIX and PMATRIX must implement a method:

void multiply(const VECTOR&, VECTOR&) const

which applies the matrix to the first argument, and returns the matrix-vector product in the second. (Note: the const is optional, but recommended.)

Definition in file GMRESR.h.

Namespaces

Functions

Detailed Description