MullerSolver2 (Apache Commons Math (Legacy) 4.0-SNAPSHOT API)

java.lang.Object
- org.apache.commons.math4.legacy.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
- - org.apache.commons.math4.legacy.analysis.solvers.AbstractUnivariateSolver
  - - org.apache.commons.math4.legacy.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 a complex number arises in the computation, we simply use its modulus as a real approximation.

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

The formulas here do not use divided differences directly.

Since:

1.2

See Also:

MullerSolver

Constructor Summary

Constructors
Constructor	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

All Methods Instance Methods Concrete Methods
Modifier and Type Method Description

protected double doSolve()
Method for implementing actual optimization algorithms in derived classes.
- Methods inherited from class org.apache.commons.math4.legacy.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.math4.legacy.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