JMSLTM Numerical Library 5.0.1

com.imsl.math
Class ZeroFunction

java.lang.Object
  extended by com.imsl.math.ZeroFunction
All Implemented Interfaces:
Serializable, Cloneable

public class ZeroFunction
extends Object
implements Serializable, Cloneable

Muller's method to find the zeros of a univariate function, f(x).

ZeroFunction computes n real zeros of a real function f. Given a user-supplied function f(x) and an n-vector of initial guesses x_1, x_2, ldots, x_n, the routine uses Muller's method to locate n real zeros of f, that is, n real values of x for which f(x) = 0. The routine has two convergence criteria: the first requires that

left| {f,left( {x_i^m } right)} right|

be less than errorAbsolute, specified by the setAbsoluteError method; the second requires that the relative change of any two successive approximations to an x_i be less than ErrorRelative, specified by the setAbsoluteError method.

Here,

x_i^m

is the m-th approximation to x_i. Let errorAbsolute be varepsilon _1, and errorRelative be varepsilon _2. The criteria may be stated mathematically as follows:

Criterion 1:

left| {f,left( {x_i^m } right)} right| 
  lt ,,varepsilon _1

Criterion 2:

left| {frac{{x_i^{m + 1}  - x_i^m }}{{x_i^m }}} 
  right|; lt ;varepsilon _2

"Convergence" is the satisfaction of either criterion.

See Also:
Example, Serialized Form

Nested Class Summary
static interface ZeroFunction.Function
          Public interface for the user supplied function to ZeroFunction.
 
Constructor Summary
ZeroFunction()
          Creates an instance of the solver.
 
Method Summary
 boolean allConverged()
          Returns true if the iterations for all of the roots have converged.
 double[] computeZeros(ZeroFunction.Function objectF, double[] guess)
          Returns the zeros of a univariate function.
 int getIterations(int nRoot)
          Returns the number of iterations used to compute a root.
 void setAbsoluteError(double errorAbsolute)
          Sets first stopping criterion.
 void setMaxIterations(int maxIterations)
          Sets the maximum number of iterations allowed per root.
 void setRelativeError(double errorRelative)
          Sets second stopping criterion is the relative error.
 void setSpread(double spread)
          Sets the spread.
 void setSpreadTolerance(double spreadTolerance)
          Sets the spread criteria for multiple zeros.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

ZeroFunction

public ZeroFunction()
Creates an instance of the solver.

Method Detail

allConverged

public boolean allConverged()
Returns true if the iterations for all of the roots have converged.


computeZeros

public double[] computeZeros(ZeroFunction.Function objectF,
                             double[] guess)
Returns the zeros of a univariate function.

Parameters:
objectF - contains the function for which the zeros will be found.
guess - a double array containing an initial guess of the zeros. A zero will be found for each point in guess.

getIterations

public int getIterations(int nRoot)
Returns the number of iterations used to compute a root.

Parameters:
nRoot - an int specifying the index of the root

setAbsoluteError

public void setAbsoluteError(double errorAbsolute)
Sets first stopping criterion. A zero x[i] is accepted if |f(x[i])| is less than this tolerance. Its default value is about 1.0e-8.

Parameters:
errorAbsolute - a double value specifying the first stopping criterion
Throws:
IllegalArgumentException - is thrown if errorAbsolute is less than 0

setMaxIterations

public void setMaxIterations(int maxIterations)
Sets the maximum number of iterations allowed per root. Its default value is 100.

Parameters:
maxIterations - an int specifying the maximum number of iterations allowed per root
Throws:
IllegalArgumentException - is thrown if maxIterations is less than zero.

setRelativeError

public void setRelativeError(double errorRelative)
Sets second stopping criterion is the relative error. A zero x[i] is accepted if the relative change of two successive approximations to x[i] is less than this tolerance. Its default value is about 1.0e-8.

Parameters:
errorRelative - a double value specifying the second stopping criterion
Throws:
IllegalArgumentException - is thrown if errorRelative is less than 0 or greater than 1

setSpread

public void setSpread(double spread)
Sets the spread. See setSpreadTolerance.

Parameters:
spread - is the new spread. Its default value is 1.0.
See Also:
setSpreadTolerance(double)

setSpreadTolerance

public void setSpreadTolerance(double spreadTolerance)
Sets the spread criteria for multiple zeros. If the zero x[i] has been computed and |x[i]-x[j]| lt spreadTolerance, where x[j] is a previously computed zero, then the computation is restarted with a guess equal to x[i]+spread. The default value for spreadTolerance is 1.0e-5.

Parameters:
spreadTolerance - a double value specifying the spread tolerance
Throws:
IllegalArgumentException - is thrown if spreadTolerance is less than zero.

JMSLTM Numerical Library 5.0.1

Copyright © 1970-2008 Visual Numerics, Inc.
Built July 8 2008.