com.imsl.math

Class ZeroFunction

java.lang.Object

com.imsl.math.ZeroFunction

All Implemented Interfaces:

Serializable, Cloneable

Deprecated.

ZeroFunction has been replaced by ZerosFunction.

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

Nested Classes

Modifier and Type	Class and Description
static interface	ZeroFunction.Function Deprecated. ZeroFunction has been replaced by ZerosFunction.

Constructor Summary

Constructors

Constructor and Description
ZeroFunction() Deprecated. Creates an instance of the solver.

Method Summary

Modifier and Type	Method and Description
boolean	allConverged() Deprecated. Returns true if the iterations for all of the roots have converged.
double[]	computeZeros(ZeroFunction.Function objectF, double[] guess) Deprecated. Returns the zeros of a univariate function.
int	getIterations(int nRoot) Deprecated. Returns the number of iterations used to compute a root.
void	setAbsoluteError(double errorAbsolute) Deprecated. Sets first stopping criterion.
void	setMaxIterations(int maxIterations) Deprecated. Sets the maximum number of iterations allowed per root.
void	setRelativeError(double errorRelative) Deprecated. Sets second stopping criterion is the relative error.
void	setSpread(double spread) Deprecated. Sets the spread.
void	setSpreadTolerance(double spreadTolerance) Deprecated. 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()

Deprecated.

Creates an instance of the solver.

Method Detail

setAbsoluteError

public void setAbsoluteError(double errorAbsolute)

Deprecated.

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

setRelativeError

public void setRelativeError(double errorRelative)

Deprecated.

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

setSpreadTolerance

public void setSpreadTolerance(double spreadTolerance)

Deprecated.

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.

setSpread

public void setSpread(double spread)

Deprecated.

Sets the spread. See setSpreadTolerance.

Parameters:

spread - is the new spread. Its default value is 1.0.

See Also:

ZeroFunction.setSpreadTolerance(double)

setMaxIterations

public void setMaxIterations(int maxIterations)

Deprecated.

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.

getIterations

public int getIterations(int nRoot)

Deprecated.

Returns the number of iterations used to compute a root.

Parameters:

nRoot - an int specifying the index of the root

allConverged

public boolean allConverged()

Deprecated.

Returns true if the iterations for all of the roots have converged.

computeZeros

public double[] computeZeros(ZeroFunction.Function objectF,
                             double[] guess)

Deprecated.

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.