# Class 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.

• ## 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

Modifier and Type
Method
Description
protected double
doSolve()
Method for implementing actual optimization algorithms in derived classes.

### Methods inherited from class org.hipparchus.analysis.solvers.BaseAbstractUnivariateSolver

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, 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.hipparchus.analysis.solvers.BaseUnivariateSolver

getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getRelativeAccuracy, solve, solve, solve
• ## Constructor Details

• ### 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 Details

• ### doSolve

protected double doSolve() throws
Method for implementing actual optimization algorithms in derived classes.
Specified by:
doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>
Returns:
the root.
Throws:
MathIllegalArgumentException - if the initial search interval does not bracket a root and the solver requires it.
MathIllegalStateException - if the maximal number of evaluations is exceeded.