public class RegulaFalsiSolver extends BaseSecantSolver
Secant method.
The Regula Falsi method is included for completeness, for testing purposes, for educational purposes, for
comparison to other algorithms, etc. It is however not intended to be used for actual problems, as
one of the bounds often remains fixed, resulting in very slow convergence. Instead, one of the well-known modified
Regula Falsi algorithms can be used (Illinois or Pegasus). These two algorithms solve the fundamental issues of
the original Regula
Falsi algorithm, and greatly out-performs it for most, if not all, (practical) functions.
Unlike the Secant method, the Regula Falsi guarantees convergence, by maintaining a bracketed
solution. Note however, that due to the finite/limited precision of Java's double type, which is used
in this implementation, the algorithm may get stuck in a situation where it no longer makes any progress. Such cases
are detected and result in a ConvergenceException exception being thrown. In other words, the algorithm
theoretically guarantees convergence, but the implementation does not.
The Regula Falsi method assumes that the function is continuous, but not necessarily smooth.
Implementation based on the following article: M. Dowell and P. Jarratt, A modified regula falsi method for computing the root of an equation, BIT Numerical Mathematics, volume 11, number 2, pages 168-174, Springer, 1971.
BaseSecantSolver.MethodDEFAULT_ABSOLUTE_ACCURACY| Constructor and Description |
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RegulaFalsiSolver()
Construct a solver with default accuracy (1e-6).
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RegulaFalsiSolver(double absoluteAccuracy)
Construct a solver.
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RegulaFalsiSolver(double relativeAccuracy,
double absoluteAccuracy)
Construct a solver.
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RegulaFalsiSolver(double relativeAccuracy,
double absoluteAccuracy,
double functionValueAccuracy)
Construct a solver.
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doSolve, solve, solve, solvecomputeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, solve, solve, verifyBracketing, verifyInterval, verifySequenceclone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, waitgetAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solvepublic RegulaFalsiSolver()
public RegulaFalsiSolver(double absoluteAccuracy)
absoluteAccuracy - Absolute accuracy.public RegulaFalsiSolver(double relativeAccuracy,
double absoluteAccuracy)
relativeAccuracy - Relative accuracy.absoluteAccuracy - Absolute accuracy.public RegulaFalsiSolver(double relativeAccuracy,
double absoluteAccuracy,
double functionValueAccuracy)
relativeAccuracy - Relative accuracy.absoluteAccuracy - Absolute accuracy.functionValueAccuracy - Maximum function value error.Copyright © 2019 CNES. All rights reserved.