Class MINRESSolver

java.lang.Object

org.ojalgo.matrix.task.iterative.IterativeSolverTask

org.ojalgo.matrix.task.iterative.MINRESSolver

All Implemented Interfaces:

MatrixTask<Double>, SolverTask<Double>

public final class MINRESSolver
extends IterativeSolverTask

Minimal Residual (MINRES) solver for symmetric (possibly indefinite) square systems.

This class mirrors the public API and internal scratch structure of QMRSolver, but implements the classic MINRES iteration specialised for symmetric matrices. Right-preconditioning is supported using the Preconditioner API provided by IterativeSolverTask. A shift parameter is present but fixed to zero in this implementation; it is retained to enable straightforward future extensions.

Characteristics

• Operates on matrix–vector products with A only (symmetry assumed).
• Right-preconditioning is applied via the Preconditioner interface.
• Stops when the residual norm is small relative to the RHS norm (or absolutely small when RHS is zero), or when the iteration limit is reached.

When to use

• For symmetric problems, including indefinite ones, where CG is not applicable.
• When a robust Krylov method without A^T products is desired.
• When right-preconditioning is convenient and a symmetric preconditioner is available.

References

• Paige, C. C., and M. A. Saunders (1975), Solutions of sparse indefinite systems of linear equations.
• Numerical Analysis. 12 (4): 617–629. doi:10.1137/0712047.

Nested Class Summary

Nested classes/interfaces inherited from class IterativeSolverTask

IterativeSolverTask.Configurator

Nested classes/interfaces inherited from interface SolverTask

SolverTask.Factory<N>

Field Summary

Fields

Modifier and Type	Field	Description
private R064Store	r1
private R064Store	r2
private R064Store	v
private R064Store	w
private R064Store	w1
private R064Store	w2
private R064Store	y

Fields inherited from class IterativeSolverTask

DEFAULT

Fields inherited from interface SolverTask

C128, H256, Q128, R064, R128

Constructor Summary

Constructors

Constructor	Description
MINRESSolver()

Method Summary

Modifier and Type	Method	Description
private static void	axpy(double alpha, R064Store x, Mutate1D.Modifiable<?> y)
private static double	norm2(R064Store a)
double	resolve(List<Equation> equations, PhysicalStore<Double> x)
private static void	scaleCopy(R064Store src, double alpha, R064Store dst)
private static void	scaleInPlace(R064Store x, double alpha)

Methods inherited from class IterativeSolverTask

configurator, debug, getAccuracyContext, getIterationsLimit, getPreconditioner, getRelaxationFactor, isDebugPrinterSet, preallocate, resolve, setAccuracyContext, setDebugPrinter, setIterationsLimit, setPreconditioner, setRelaxationFactor, solve, solve, toListOfRows, worker

Methods inherited from class Object

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

Methods inherited from interface SolverTask

preallocate, solve, toSolutionProvider

Field Details

r1

private R064Store r1

r2

private R064Store r2

v

private R064Store v

y

private R064Store y

w

private R064Store w

w1

private R064Store w1

w2

private R064Store w2

Constructor Details

MINRESSolver

public MINRESSolver()

Method Details

axpy

private static void axpy(double alpha,
 R064Store x,
 Mutate1D.Modifiable<?> y)

norm2

private static double norm2(R064Store a)

scaleCopy

private static void scaleCopy(R064Store src,
 double alpha,
 R064Store dst)

scaleInPlace

private static void scaleInPlace(R064Store x,
 double alpha)

resolve

public double resolve(List<Equation> equations,
 PhysicalStore<Double> x)

Specified by:

resolve in class IterativeSolverTask