Class MullerSolver

  extended by org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
      extended by org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver
          extended by org.apache.commons.math3.analysis.solvers.MullerSolver
All Implemented Interfaces:
BaseUnivariateSolver<UnivariateFunction>, UnivariateSolver

public class MullerSolver
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.

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.

$Id: 1391927 2012-09-30 00:03:30Z erans $
See Also:

Constructor Summary
          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.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


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


public MullerSolver(double absoluteAccuracy)
Construct a solver.

absoluteAccuracy - Absolute accuracy.


public MullerSolver(double relativeAccuracy,
                    double absoluteAccuracy)
Construct a solver.

relativeAccuracy - Relative accuracy.
absoluteAccuracy - Absolute accuracy.
Method Detail


protected double doSolve()
                  throws TooManyEvaluationsException,
Method for implementing actual optimization algorithms in derived classes.

Specified by:
doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>
the root.
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.

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