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<div class="subTitle">org.apache.commons.math3.analysis.solvers</div>
<h2 title="Class MullerSolver2" class="title">Class MullerSolver2</h2>
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<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>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>&gt;</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>
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<li>org.apache.commons.math3.analysis.solvers.MullerSolver2</li>
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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>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>&gt;, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">UnivariateSolver</a></dd>
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<pre>public class <span class="strong">MullerSolver2</span>
extends <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AbstractUnivariateSolver.html" title="class in org.apache.commons.math3.analysis.solvers">AbstractUnivariateSolver</a></pre>
<div class="block">This class implements the <a href="http://mathworld.wolfram.com/MullersMethod.html">
Muller's Method</a> for root finding of real univariate functions. For
reference, see <b>Elementary Numerical Analysis</b>, ISBN 0070124477,
chapter 3.
<p>
Muller's method applies to both real and complex functions, but here we
restrict ourselves to real functions.
This class differs from <a href="../../../../../../org/apache/commons/math3/analysis/solvers/MullerSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><code>MullerSolver</code></a> in the way it avoids complex
operations.</p>
Except for the initial [min, max], it does not require bracketing
condition, e.g. f(x0), f(x1), f(x2) can have the same sign. If complex
number arises in the computation, we simply use its modulus as real
approximation.</p>
<p>
Because the interval may not be bracketing, bisection alternative is
not applicable here. However in practice our treatment usually works
well, especially near real zeroes where the imaginary part of complex
approximation is often negligible.</p>
<p>
The formulas here do not use divided differences directly.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>1.2</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: MullerSolver2.java 1379560 2012-08-31 19:40:30Z erans $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/solvers/MullerSolver.html" title="class in org.apache.commons.math3.analysis.solvers"><code>MullerSolver</code></a></dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/MullerSolver2.html#MullerSolver2()">MullerSolver2</a></strong>()</code>
<div class="block">Construct a solver with default accuracy (1e-6).</div>
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<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/MullerSolver2.html#MullerSolver2(double)">MullerSolver2</a></strong>(double&nbsp;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/MullerSolver2.html#MullerSolver2(double, double)">MullerSolver2</a></strong>(double&nbsp;relativeAccuracy,
double&nbsp;absoluteAccuracy)</code>
<div class="block">Construct a solver.</div>
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<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/MullerSolver2.html#doSolve()">doSolve</a></strong>()</code>
<div class="block">Method for implementing actual optimization algorithms in derived
classes.</div>
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<h3>Methods inherited from class&nbsp;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#solve(int, FUNC, double, 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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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<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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<h3>Methods inherited from interface&nbsp;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>, <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseUnivariateSolver.html#solve(int, FUNC, double, double, double)">solve</a></code></li>
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<h4>MullerSolver2</h4>
<pre>public&nbsp;MullerSolver2()</pre>
<div class="block">Construct a solver with default accuracy (1e-6).</div>
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<pre>public&nbsp;MullerSolver2(double&nbsp;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>
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<h4>MullerSolver2</h4>
<pre>public&nbsp;MullerSolver2(double&nbsp;relativeAccuracy,
double&nbsp;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>
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<h4>doSolve</h4>
<pre>protected&nbsp;double&nbsp;doSolve()
throws <a href="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre>
<div class="block">Method for implementing actual optimization algorithms in derived
classes.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html#doSolve()">doSolve</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/analysis/solvers/BaseAbstractUnivariateSolver.html" title="class in org.apache.commons.math3.analysis.solvers">BaseAbstractUnivariateSolver</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>&gt;</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the root.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</a></code> - if the maximal number of evaluations
is exceeded.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the initial search interval does not bracket
a root and the solver requires it.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code></dd></dl>
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