com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner
Class SsorPreconditioner

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner.SsorPreconditioner

All Implemented Interfaces:

Preconditioner

public class SsorPreconditioner
extends java.lang.Object
implements Preconditioner

SSOR preconditioner is derived from the symmetric coefficient matrix A which is decomposed as

A = D + L + L^t

The SSOR preconditioning matrix is defined as

M = (D + L)D^-1(D + L)^t

or, parameterized by ω

M(ω) = (1/(2 - ω))(D / ω + L)(D / ω)^-1(D / ω + L)^t

The optimal value of ω will reduce the number of iterations to a lower order. However, in practice, the spectral information for computing the optimal ω is expensive to obtain.

See Also:

SymmetricSuccessiveOverrelaxationSolver

Constructor Summary

SsorPreconditioner(Matrix A, double omega)
Create a SSOR preconditioner with a symmetric coefficient matrix.

Method Summary

Vector	solve(Vector x) Solve Mz = x using this SSOR preconditioner.
Vector	transposeSolve(Vector x) M-tx = M-1x because M is symmetric.

Methods inherited from class java.lang.Object

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

Constructor Detail

SsorPreconditioner

public SsorPreconditioner(Matrix A,
                          double omega)

Create a SSOR preconditioner with a symmetric coefficient matrix.

Parameters:

A - the symmetric coefficient matrix

omega - the extrapolation factor

Method Detail

solve

public Vector solve(Vector x)

Solve Mz = x using this SSOR preconditioner.

Specified by:

solve in interface Preconditioner

Parameters:

x -

Returns:

M^-1x

transposeSolve

public Vector transposeSolve(Vector x)

M^-tx = M^-1x because M is symmetric.

Specified by:

transposeSolve in interface Preconditioner

Parameters:

x - the input Vector

Returns:

solve(x)