org.apache.commons.math3.analysis.solvers

## Class 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.

Since:
1.2
Version:
\$Id: MullerSolver.java 1244107 2012-02-14 16:17:55Z erans \$
`MullerSolver2`
• ### Constructor Summary

Constructors
Constructor and Description
`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

Methods
Modifier and Type Method and Description
`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

• #### 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 `BaseAbstractUnivariateSolver<UnivariateFunction>`
Returns:
the root.