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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.analysis.solvers;
/**
* Implements the <em>Regula Falsi</em> or <em>False position</em> method for
* root-finding (approximating a zero of a univariate real function). It is a
* modified {@link SecantSolver <em>Secant</em>} method.
*
* <p>The <em>Regula Falsi</em> method is included for completeness, for
* testing purposes, for educational purposes, for comparison to other
* algorithms, etc. It is however <strong>not</strong> 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
* <em>Regula Falsi</em> algorithms can be used ({@link IllinoisSolver
* <em>Illinois</em>} or {@link PegasusSolver <em>Pegasus</em>}). These two
* algorithms solve the fundamental issues of the original <em>Regula
* Falsi</em> algorithm, and greatly out-performs it for most, if not all,
* (practical) functions.
*
* <p>Unlike the <em>Secant</em> method, the <em>Regula Falsi</em> guarantees
* convergence, by maintaining a bracketed solution. Note however, that due to
* the finite/limited precision of Java's {@link Double 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 {@code ConvergenceException} exception being thrown. In other words,
* the algorithm theoretically guarantees convergence, but the implementation
* does not.</p>
*
* <p>The <em>Regula Falsi</em> method assumes that the function is continuous,
* but not necessarily smooth.</p>
*
* <p>Implementation based on the following article: M. Dowell and P. Jarratt,
* <em>A modified regula falsi method for computing the root of an
* equation</em>, BIT Numerical Mathematics, volume 11, number 2,
* pages 168-174, Springer, 1971.</p>
*
* @since 3.0
*/
public class RegulaFalsiSolver extends BaseSecantSolver {
/** Construct a solver with default accuracy (1e-6). */
public RegulaFalsiSolver() {
super(DEFAULT_ABSOLUTE_ACCURACY, Method.REGULA_FALSI);
}
/**
* Construct a solver.
*
* @param absoluteAccuracy Absolute accuracy.
*/
public RegulaFalsiSolver(final double absoluteAccuracy) {
super(absoluteAccuracy, Method.REGULA_FALSI);
}
/**
* Construct a solver.
*
* @param relativeAccuracy Relative accuracy.
* @param absoluteAccuracy Absolute accuracy.
*/
public RegulaFalsiSolver(final double relativeAccuracy,
final double absoluteAccuracy) {
super(relativeAccuracy, absoluteAccuracy, Method.REGULA_FALSI);
}
/**
* Construct a solver.
*
* @param relativeAccuracy Relative accuracy.
* @param absoluteAccuracy Absolute accuracy.
* @param functionValueAccuracy Maximum function value error.
*/
public RegulaFalsiSolver(final double relativeAccuracy,
final double absoluteAccuracy,
final double functionValueAccuracy) {
super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy, Method.REGULA_FALSI);
}
}