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

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

All Implemented Interfaces:

IterativeSolver

public class BiconjugateGradientStabilizedSolver
extends java.lang.Object
implements IterativeSolver

The Biconjugate Gradient Stabilized (BiCGSTAB) method is useful for solving non-symmetric n-by-n linear systems. This algorithm is a transpose-free variant of BiCG, like CGS, but using different updates for the A^T-sequence in order to obtain smoother tolerance than CGS.

Only left preconditioning is supported in this implementation.

See Also:

"Yousef Saad, “BICGSTAB,” in Iterative Methods for Sparse Linear Systems, 2nd ed. 2000, ch. 7, sec. 7.4.2, p. 216-219."

Nested Class Summary

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

IterativeSolver.ConvergenceFailure, IterativeSolver.Problem

Field Summary

static int

DEFAULT_RESIDUAL_REFRESH_RATE The algorithm recomputes the residual as b - Axi once per this number of iterations

Constructor Summary

BiconjugateGradientStabilizedSolver()

BiconjugateGradientStabilizedSolver(int residualRefreshRate)
The solver recomputes the residual as b - Ax_i once per this number of iterations

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

Field Detail

DEFAULT_RESIDUAL_REFRESH_RATE

public static final int DEFAULT_RESIDUAL_REFRESH_RATE

The algorithm recomputes the residual as b - Ax_i once per this number of iterations

See Also:

Constant Field Values

Constructor Detail

BiconjugateGradientStabilizedSolver

public BiconjugateGradientStabilizedSolver()

BiconjugateGradientStabilizedSolver

public BiconjugateGradientStabilizedSolver(int residualRefreshRate)

The solver recomputes the residual as b - Ax_i once per this number of iterations

Parameters:

residualRefreshRate - the number of iterations before the next refresh

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