org.apache.commons.math3.analysis.solvers
Class PegasusSolver

java.lang.Object
  org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
      org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver
          org.apache.commons.math3.analysis.solvers.BaseSecantSolver
              org.apache.commons.math3.analysis.solvers.PegasusSolver

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, BracketedUnivariateSolver<UnivariateFunction>, UnivariateSolver

public class PegasusSolver
extends BaseSecantSolver

Implements the Pegasus method for root-finding (approximating a zero of a univariate real function). It is a modified Regula Falsi method.

Like the Regula Falsi method, convergence is guaranteed by maintaining a bracketed solution. The Pegasus method however, should converge much faster than the original Regula Falsi method. Furthermore, this implementation of the Pegasus method should not suffer from the same implementation issues as the Regula Falsi method, which may fail to convergence in certain cases. Also, the Pegasus method should converge faster than the Illinois method, another Regula Falsi-based method.

The Pegasus method assumes that the function is continuous, but not necessarily smooth.

Implementation based on the following article: M. Dowell and P. Jarratt, The "Pegasus" method for computing the root of an equation, BIT Numerical Mathematics, volume 12, number 4, pages 503-508, Springer, 1972.

Since:

3.0

Version:

$Id: PegasusSolver.java 3720 2012-03-16 16:34:17Z CardosoP $

Nested Class Summary

Nested classes/interfaces inherited from class org.apache.commons.math3.analysis.solvers.BaseSecantSolver

BaseSecantSolver.Method

Field Summary

Fields inherited from class org.apache.commons.math3.analysis.solvers.BaseSecantSolver

DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

PegasusSolver()
Construct a solver with default accuracy (1e-6).

PegasusSolver(double absoluteAccuracy)
Construct a solver.

PegasusSolver(double relativeAccuracy, double absoluteAccuracy)
Construct a solver.

PegasusSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)
Construct a solver.

Method Summary

Methods inherited from class org.apache.commons.math3.analysis.solvers.BaseSecantSolver

doSolve, solve, solve, solve

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, 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

Constructor Detail

PegasusSolver

public PegasusSolver()

Construct a solver with default accuracy (1e-6).

PegasusSolver

public PegasusSolver(double absoluteAccuracy)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

PegasusSolver

public PegasusSolver(double relativeAccuracy,
                     double absoluteAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

PegasusSolver

public PegasusSolver(double relativeAccuracy,
                     double absoluteAccuracy,
                     double functionValueAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

functionValueAccuracy - Maximum function value error.