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## 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 1379560 2012-08-31 19:40:30Z erans $
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`

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