com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.stationary
Class SymmetricSuccessiveOverrelaxationSolver

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.stationary.SymmetricSuccessiveOverrelaxationSolver

All Implemented Interfaces:

IterativeSolver

public class SymmetricSuccessiveOverrelaxationSolver
extends java.lang.Object
implements IterativeSolver

The Symmetric Successive Overrelaxation method (SSOR) is like SOR, but it performs in each iteration one forward sweep followed by one backward sweep.

With an optimal value of ω, the convergence rate of SSOR is usually slower than that of SOR with an optimal ω.

Preconditioning is not supported in this solver.

See Also:

Wikipedia: Successive over-relaxation method

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

SymmetricSuccessiveOverrelaxationSolver(double omega)
Construct a SSOR solver with the extrapolation factor ω.

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

SymmetricSuccessiveOverrelaxationSolver

public SymmetricSuccessiveOverrelaxationSolver(double omega)

Construct a SSOR solver with the extrapolation factor ω.

Parameters:

omega - the extrapolation factor

See Also:

SuccessiveOverrelaxationSolver.SuccessiveOverrelaxationSolver(double)

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