Description of qmr

qmr		Programmers Guide
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Category:itl,algorithms

Component type:function

Prototype

template <class Matrix, class Vector, class VectorB, class Precond1, class Precond2, class Iteration> int qmr(const Matrix &A, Vector &x, const VectorB &b, const Precond1 &M1, const Precond2 &M2, Iteration& iter) ;

Description

This routine solves the unsymmetric linear system Ax = b using the Quasi-Minimal Residual method.

return value	meaning
0	convergence within maximum iterations
1	no convergence after maximum iterations
2	breakdown in rho
3	breakdown in beta
4	breakdown in gamma
5	breakdown in delta
6	breakdown in ep
7	breakdown in xi

See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual method for non-Hermitian linear systems, Numerical Math., 60(1991), pp. 315-339

Definition

qmr.h

Preconditions

Complexity

Example

In qmr.cc:

  Matrix A(5, 5);
  // Fill matrix...
  dense1D<Type> x(A.nrows(), Type(0));
  dense1D<Type> b(A.ncols());
  for (dense1D<Type>::iterator i=b.begin(); i!=b.end(); i++)
    *i = 1.;

  //SSOR preconditioner
  SSOR<Matrix> precond(A);
  //iteration
  noisy_iteration<double> iter(b, max_iter, 1e-6);
  //qmr algorithm
  qmr(A, x, b, precond.left(), precond.right(), iter);

Notes

See also