Class MullerSolver
- All Implemented Interfaces:
BaseUnivariateSolver<UnivariateFunction>
,UnivariateSolver
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
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final double
Default absolute accuracy. -
Constructor Summary
ConstructorsConstructorDescriptionConstruct a solver with default accuracy (1e-6).MullerSolver
(double absoluteAccuracy) Construct a solver.MullerSolver
(double relativeAccuracy, double absoluteAccuracy) Construct a solver. -
Method Summary
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
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Field Details
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DEFAULT_ABSOLUTE_ACCURACY
private static final double DEFAULT_ABSOLUTE_ACCURACYDefault absolute accuracy.- See Also:
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Constructor Details
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MullerSolver
public MullerSolver()Construct a solver with default accuracy (1e-6). -
MullerSolver
public MullerSolver(double absoluteAccuracy) Construct a solver.- Parameters:
absoluteAccuracy
- Absolute accuracy.
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MullerSolver
public MullerSolver(double relativeAccuracy, double absoluteAccuracy) Construct a solver.- Parameters:
relativeAccuracy
- Relative accuracy.absoluteAccuracy
- Absolute accuracy.
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Method Details
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doSolve
protected double doSolve() throws TooManyEvaluationsException, NumberIsTooLargeException, NoBracketingExceptionMethod for implementing actual optimization algorithms in derived classes.- Specified by:
doSolve
in classBaseAbstractUnivariateSolver<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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solve
private double solve(double min, double max, double fMin, double fMax) throws TooManyEvaluationsException Find a real root in the given interval.- Parameters:
min
- Lower bound for the interval.max
- Upper bound for the interval.fMin
- function value at the lower bound.fMax
- function value at the upper bound.- Returns:
- the point at which the function value is zero.
- Throws:
TooManyEvaluationsException
- if the allowed number of calls to the function to be solved has been exhausted.
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