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

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

All Implemented Interfaces:

IterativeLinearSystemSolver

public class SteepestDescentSolver
extends java.lang.Object
implements IterativeLinearSystemSolver

The Steepest Descent method (SDM) solves a symmetric n-by-n linear system. The convergence is guaranteed if A is symmetric positive definite.

Only left preconditioning is supported in this implementation. The preconditioner must be symmetric and positive definite.

See Also:

Wikipedia: Gradient descent

Nested Class Summary

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

IterativeLinearSystemSolver.Solution

Field Summary

static int

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

Constructor Summary

SteepestDescentSolver(int maxIteration, Tolerance tolerance)
Construct a Steepest Descent method (SDM) solver.

SteepestDescentSolver(PreconditionerFactory leftPreconditionerFactory, int residualRefreshRate, int maxIteration, Tolerance tolerance)
Construct a Steepest Descent method (SDM) solver.

Method Summary

IterativeLinearSystemSolver.Solution	solve(LSProblem problem)
IterativeLinearSystemSolver.Solution	solve(LSProblem problem, IterationMonitor<Vector> monitor) Solves iteratively Ax = b until the solution converges, i.e., the norm of residual (b - Ax) is less than or equal to the threshold.

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

SteepestDescentSolver

public SteepestDescentSolver(PreconditionerFactory leftPreconditionerFactory,
                             int residualRefreshRate,
                             int maxIteration,
                             Tolerance tolerance)

Construct a Steepest Descent method (SDM) solver.

Parameters:

leftPreconditionerFactory - constructs a new left preconditioner

residualRefreshRate - the number of iterations before the next refresh

maxIteration - the maximum number of iterations

tolerance - the convergence threshold

SteepestDescentSolver

public SteepestDescentSolver(int maxIteration,
                             Tolerance tolerance)

Construct a Steepest Descent method (SDM) solver.

Parameters:

maxIteration - the maximum number of iterations

tolerance - the convergence threshold

Method Detail

solve

public IterativeLinearSystemSolver.Solution solve(LSProblem problem)
                                           throws ConvergenceFailure

Throws:

ConvergenceFailure

solve

public IterativeLinearSystemSolver.Solution solve(LSProblem problem,
                                                  IterationMonitor<Vector> monitor)
                                           throws ConvergenceFailure

Description copied from interface: IterativeLinearSystemSolver

Solves iteratively

Ax = b

until the solution converges, i.e., the norm of residual (b - Ax) is less than or equal to the threshold.

Specified by:

solve in interface IterativeLinearSystemSolver

Parameters:

problem - a system of linear equations

monitor - an iteration monitor

Returns:

an (approximate) solution to the linear problem

Throws:

ConvergenceFailure - if the algorithm fails to converge