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 MathIllegalStateException 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.MethodBracketedUnivariateSolver.IntervalDEFAULT_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, doSolveInterval, solve, solve, solve, solveIntervalcomputeObjectiveValue, 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, waitsolveIntervalgetAbsoluteAccuracy, 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 © 2016-2021 CS GROUP. All rights reserved.