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| <div class="subTitle">org.apache.commons.math3.analysis.solvers</div> |
| <h2 title="Class RegulaFalsiSolver" class="title">Class RegulaFalsiSolver</h2> |
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| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html" title="class in org.apache.commons.math3.analysis.solvers">org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver</a><<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>></li> |
| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/analysis/solvers/AbstractUnivariateSolver.html" title="class in org.apache.commons.math3.analysis.solvers">org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html" title="class in org.apache.commons.math3.analysis.solvers">org.apache.commons.math3.analysis.solvers.BaseSecantSolver</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li>org.apache.commons.math3.analysis.solvers.RegulaFalsiSolver</li> |
| </ul> |
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| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">BaseUnivariateSolver</a><<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">BracketedUnivariateSolver</a><<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">UnivariateSolver</a></dd> |
| </dl> |
| <hr> |
| <br> |
| <pre>public class <span class="strong">RegulaFalsiSolver</span> |
| extends <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html" title="class in org.apache.commons.math3.analysis.solvers">BaseSecantSolver</a></pre> |
| <div class="block">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 <a href="../../../../../../org/apache/commons/math3/analysis/solvers/SecantSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><code><em>Secant</em></code></a> 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 (<a href="../../../../../../org/apache/commons/math3/analysis/solvers/IllinoisSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><code><em>Illinois</em></code></a> or <a href="../../../../../../org/apache/commons/math3/analysis/solvers/PegasusSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><code><em>Pegasus</em></code></a>). 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 <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><code>double</code></a> 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</code> 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></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: RegulaFalsiSolver.java 1364387 2012-07-22 18:14:11Z tn $</dd></dl> |
| </li> |
| </ul> |
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| <h3>Nested classes/interfaces inherited from class org.apache.commons.math3.analysis.solvers.<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html" title="class in org.apache.commons.math3.analysis.solvers">BaseSecantSolver</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.Method.html" title="enum in org.apache.commons.math3.analysis.solvers">BaseSecantSolver.Method</a></code></li> |
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| <code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html#DEFAULT_ABSOLUTE_ACCURACY">DEFAULT_ABSOLUTE_ACCURACY</a></code></li> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/RegulaFalsiSolver.html#RegulaFalsiSolver()">RegulaFalsiSolver</a></strong>()</code> |
| <div class="block">Construct a solver with default accuracy (1e-6).</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/RegulaFalsiSolver.html#RegulaFalsiSolver(double)">RegulaFalsiSolver</a></strong>(double absoluteAccuracy)</code> |
| <div class="block">Construct a solver.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/RegulaFalsiSolver.html#RegulaFalsiSolver(double, double)">RegulaFalsiSolver</a></strong>(double relativeAccuracy, |
| double absoluteAccuracy)</code> |
| <div class="block">Construct a solver.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/RegulaFalsiSolver.html#RegulaFalsiSolver(double, double, double)">RegulaFalsiSolver</a></strong>(double relativeAccuracy, |
| double absoluteAccuracy, |
| double functionValueAccuracy)</code> |
| <div class="block">Construct a solver.</div> |
| </td> |
| </tr> |
| </table> |
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| <h3>Methods inherited from class org.apache.commons.math3.analysis.solvers.<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html" title="class in org.apache.commons.math3.analysis.solvers">BaseSecantSolver</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html#doSolve()">doSolve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html#solve(int, org.apache.commons.math3.analysis.UnivariateFunction, double, double, org.apache.commons.math3.analysis.solvers.AllowedSolution)">solve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html#solve(int, org.apache.commons.math3.analysis.UnivariateFunction, double, double, double)">solve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseSecantSolver.html#solve(int, org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, org.apache.commons.math3.analysis.solvers.AllowedSolution)">solve</a></code></li> |
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| <h3>Methods inherited from class org.apache.commons.math3.analysis.solvers.<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html" title="class in org.apache.commons.math3.analysis.solvers">BaseAbstractUnivariateSolver</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#computeObjectiveValue(double)">computeObjectiveValue</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getAbsoluteAccuracy()">getAbsoluteAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getFunctionValueAccuracy()">getFunctionValueAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getMax()">getMax</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getMin()">getMin</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getRelativeAccuracy()">getRelativeAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#getStartValue()">getStartValue</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#incrementEvaluationCount()">incrementEvaluationCount</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#isBracketing(double, double)">isBracketing</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#isSequence(double, double, double)">isSequence</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#setup(int, FUNC, double, double, double)">setup</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#solve(int, FUNC, double)">solve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#solve(int, FUNC, double, double)">solve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#verifyBracketing(double, double)">verifyBracketing</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#verifyInterval(double, double)">verifyInterval</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#verifySequence(double, double, double)">verifySequence</a></code></li> |
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| <code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
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| </a> |
| <h3>Methods inherited from interface org.apache.commons.math3.analysis.solvers.<a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">BaseUnivariateSolver</a></h3> |
| <code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#getAbsoluteAccuracy()">getAbsoluteAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#getFunctionValueAccuracy()">getFunctionValueAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#getRelativeAccuracy()">getRelativeAccuracy</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#solve(int, FUNC, double)">solve</a>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#solve(int, FUNC, double, double)">solve</a></code></li> |
| </ul> |
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| <a name="RegulaFalsiSolver()"> |
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| </a> |
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| <h4>RegulaFalsiSolver</h4> |
| <pre>public RegulaFalsiSolver()</pre> |
| <div class="block">Construct a solver with default accuracy (1e-6).</div> |
| </li> |
| </ul> |
| <a name="RegulaFalsiSolver(double)"> |
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| </a> |
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| <h4>RegulaFalsiSolver</h4> |
| <pre>public RegulaFalsiSolver(double absoluteAccuracy)</pre> |
| <div class="block">Construct a solver.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>absoluteAccuracy</code> - Absolute accuracy.</dd></dl> |
| </li> |
| </ul> |
| <a name="RegulaFalsiSolver(double, double)"> |
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| <h4>RegulaFalsiSolver</h4> |
| <pre>public RegulaFalsiSolver(double relativeAccuracy, |
| double absoluteAccuracy)</pre> |
| <div class="block">Construct a solver.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>relativeAccuracy</code> - Relative accuracy.</dd><dd><code>absoluteAccuracy</code> - Absolute accuracy.</dd></dl> |
| </li> |
| </ul> |
| <a name="RegulaFalsiSolver(double, double, double)"> |
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| <h4>RegulaFalsiSolver</h4> |
| <pre>public RegulaFalsiSolver(double relativeAccuracy, |
| double absoluteAccuracy, |
| double functionValueAccuracy)</pre> |
| <div class="block">Construct a solver.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>relativeAccuracy</code> - Relative accuracy.</dd><dd><code>absoluteAccuracy</code> - Absolute accuracy.</dd><dd><code>functionValueAccuracy</code> - Maximum function value error.</dd></dl> |
| </li> |
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