org.apache.commons.math3.analysis.solvers
Class MullerSolver2

java.lang.Object
  org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
      org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver
          org.apache.commons.math3.analysis.solvers.MullerSolver2

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, UnivariateSolver

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 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

MullerSolver

Constructor Summary

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

protected double

doSolve() Method for implementing actual optimization algorithms in derived classes.

Methods inherited from class org.apache.commons.math3.analysis.solvers.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 org.apache.commons.math3.analysis.solvers.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()
                  throws TooManyEvaluationsException,
                         NumberIsTooLargeException,
                         NoBracketingException

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Returns:

the root.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

NoBracketingException - if the initial search interval does not bracket a root and the solver requires it.

NumberIsTooLargeException