org.apache.commons.math.analysis.solvers
Class MullerSolver

java.lang.Object
  org.apache.commons.math.analysis.solvers.BaseAbstractUnivariateRealSolver<UnivariateRealFunction>
      org.apache.commons.math.analysis.solvers.AbstractUnivariateRealSolver
          org.apache.commons.math.analysis.solvers.MullerSolver

All Implemented Interfaces:

BaseUnivariateRealSolver<UnivariateRealFunction>, UnivariateRealSolver

public class MullerSolver
extends AbstractUnivariateRealSolver

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.

Muller's original method would have function evaluation at complex point. Since our f(x) is real, we have to find ways to avoid that. Bracketing condition is one way to go: by requiring bracketing in every iteration, the newly computed approximation is guaranteed to be real.

Normally Muller's method converges quadratically in the vicinity of a zero, however it may be very slow in regions far away from zeros. For example, f(x) = exp(x) - 1, min = -50, max = 100. In such case we use bisection as a safety backup if it performs very poorly.

The formulas here use divided differences directly.

Since:

1.2

Version:

$Id: MullerSolver.java 1183138 2011-10-13 22:21:04Z erans $

See Also:

MullerSolver2

Constructor Summary

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

MullerSolver(double absoluteAccuracy)
Construct a solver.

MullerSolver(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.math.analysis.solvers.BaseAbstractUnivariateRealSolver

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.math.analysis.solvers.BaseUnivariateRealSolver

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

Constructor Detail

MullerSolver

public MullerSolver()

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

MullerSolver

public MullerSolver(double absoluteAccuracy)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

MullerSolver

public MullerSolver(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 BaseAbstractUnivariateRealSolver<UnivariateRealFunction>

Returns:

the root.