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 wellknown 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 outperforms 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 168174, Springer, 1971.
BaseSecantSolver.Method
DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description 

RegulaFalsiSolver()
Construct a solver with default accuracy (1e6).

RegulaFalsiSolver(double absoluteAccuracy)
Construct a solver.

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

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

doSolve, solve, solve, solve
computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, solve, solve, verifyBracketing, verifyInterval, verifySequence
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve
public 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 © 2003–2016 The Apache Software Foundation. All rights reserved.