com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.nonstationary
Class GeneralizedConjugateResidualSolver

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.nonstationary.GeneralizedConjugateResidualSolver

All Implemented Interfaces:

IterativeSolver

public class GeneralizedConjugateResidualSolver
extends java.lang.Object
implements IterativeSolver

The Generalized Conjugate Residual method (GCR) is useful for solving non-symmetric n-by-n linear systems, like GMRES. GCR computes the next Krylov basis vector as a linear combination of the current residual and all previous basis vectors.

This solver implements a restarted version of GCR.

Only left preconditioning is supported in this implementation.

See Also:

"Yousef Saad, “GCR, ORTHOMIN, and ORTHODIR,” in Iterative Methods for Sparse Linear Systems, 2nd ed. 2000, ch. 6, sec. 6.9, p. 182-184."

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.IterativeSolver

IterativeSolver.ConvergenceFailure, IterativeSolver.Problem

Constructor Summary

GeneralizedConjugateResidualSolver()
Create a full GCR solver.

GeneralizedConjugateResidualSolver(int m)
Create a restart version of GCR solver with the restart parameter m.

Method Summary

Vector	solve(IterativeSolver.Problem problem) Solve iteratively Ax = b until the solution is close enough, i.e., the norm of residual (b - Ax) is less than or equal to the specified iteration.
Vector	solve(IterativeSolver.Problem problem, IterationMonitor monitor) Solve iteratively Ax = b until the solution is close enough, i.e., the norm of residual (b - Ax) is less than or equal to the specified iteration.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GeneralizedConjugateResidualSolver

public GeneralizedConjugateResidualSolver()

Create a full GCR solver.

GeneralizedConjugateResidualSolver

public GeneralizedConjugateResidualSolver(int m)

Create a restart version of GCR solver with the restart parameter m.

Parameters:

m - the solver restarts for every m iterations

Method Detail

solve

public Vector solve(IterativeSolver.Problem problem)
             throws IterativeSolver.ConvergenceFailure

Description copied from interface: IterativeSolver

Solve iteratively

Ax = b

until the solution is close enough, i.e., the norm of residual (b - Ax) is less than or equal to the specified iteration.

Specified by:

solve in interface IterativeSolver

Parameters:

problem - the problem of solving Ax = b

Returns:

the computed solution for the problem

Throws:

IterativeSolver.ConvergenceFailure - if the algorithm fails to converge

solve

public Vector solve(IterativeSolver.Problem problem,
                    IterationMonitor monitor)
             throws IterativeSolver.ConvergenceFailure

Description copied from interface: IterativeSolver

Solve iteratively

Ax = b

until the solution is close enough, i.e., the norm of residual (b - Ax) is less than or equal to the specified iteration.

In each iteration, the newly computed iterate is added to the IterationMonitor for statistics or diagnostic purpose.

Specified by:

solve in interface IterativeSolver

Parameters:

problem - the problem of solving Ax = b

monitor - an IterationMonitor instance

Returns:

the computed solution for the problem

Throws:

IterativeSolver.ConvergenceFailure - if the algorithm fails to converge