fr.cnes.sirius.patrius.math.analysis.solver

Class MullerSolver2

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.solver.BaseAbstractUnivariateSolver<UnivariateFunction>

fr.cnes.sirius.patrius.math.analysis.solver.AbstractUnivariateSolver

fr.cnes.sirius.patrius.math.analysis.solver.MullerSolver2

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, UnivariateSolver, Serializable

public class MullerSolver2
extends AbstractUnivariateSolver

This class implements the Muller's Method for root finding of real univariate functions. For reference, see Elementary Numerical Analysis, ISBN 0070124477, chapter 3.

Muller's method applies to both real and complex functions, but here we restrict ourselves to real functions. This class differs from MullerSolver in the way it avoids complex operations.

Except for the initial [min, max], it does not require bracketing condition, e.g. f(x0), f(x1), f(x2) can have the same sign. If complex number arises in the computation, we simply use its modulus as real approximation.

Because the interval may not be bracketing, bisection alternative is not applicable here. However in practice our treatment usually works well, especially near real zeroes where the imaginary part of complex approximation is often negligible.

The formulas here do not use divided differences directly.

Since:

1.2

Version:

$Id: MullerSolver2.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

MullerSolver, Serialized Form

Constructor Summary

Constructors

Constructor and Description
MullerSolver2() Construct a solver with default accuracy (1e-6).
MullerSolver2(double absoluteAccuracy) Construct a solver.
MullerSolver2(double relativeAccuracy, double absoluteAccuracy) Construct a solver.

Method Summary

Modifier and Type	Method and Description
protected double	doSolve() Method for implementing actual optimization algorithms in derived classes.

Methods inherited from class fr.cnes.sirius.patrius.math.analysis.solver.BaseAbstractUnivariateSolver

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, solve, solve, solve, verifyBracketing, verifyInterval, verifySequence

Methods inherited from class java.lang.Object

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

Methods inherited from interface fr.cnes.sirius.patrius.math.analysis.solver.BaseUnivariateSolver

getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve

Constructor Detail

MullerSolver2

public MullerSolver2()

Construct a solver with default accuracy (1e-6).

MullerSolver2

public MullerSolver2(double absoluteAccuracy)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

MullerSolver2

public MullerSolver2(double relativeAccuracy,
                     double absoluteAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

Method Detail

doSolve

protected double doSolve()

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Returns:

the root.