com.imsl.math

Class ZeroPolynomial

java.lang.Object

com.imsl.math.ZeroPolynomial

All Implemented Interfaces:

Serializable, Cloneable

public class ZeroPolynomial
extends Object
implements Serializable, Cloneable

The ZeroPolynomial class computes the zeros of a polynomial with complex coefficients, Aberth's method. This class is a Java translation of a Fortran code written by Dario Andrea Bini, University of Pisa, Italy (bini@dm.unipi.it). Numerical computation of polynomial zeros by means of Aberth's method, Numerical Algorithms, 13 (1996), pp. 179-200. The original Fortran code includes the following notice.

All the software contained in this library is protected by copyright Permission to use, copy, modify, and distribute this software for any purpose without fee is hereby granted, provided that this entire notice is included in all copies of any software which is or includes a copy or modification of this software and in all copies of the supporting documentation for such software.

THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED WARRANTY. IN NO EVENT, NEITHER THE AUTHORS, NOR THE PUBLISHER, NOR ANY MEMBER OF THE EDITORIAL BOARD OF THE JOURNAL "NUMERICAL ALGORITHMS", NOR ITS EDITOR-IN-CHIEF, BE LIABLE FOR ANY ERROR IN THE SOFTWARE, ANY MISUSE OF IT OR ANY DAMAGE ARISING OUT OF ITS USE. THE ENTIRE RISK OF USING THE SOFTWARE LIES WITH THE PARTY DOING SO. ANY USE OF THE SOFTWARE CONSTITUTES ACCEPTANCE OF THE TERMS OF THE ABOVE STATEMENT.

See Also:

Real coefficients Example, Complex coefficients Example, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ZeroPolynomial.DidNotConvergeException The iteration did not converge

Field Summary

Fields

Modifier and Type	Field and Description
static double	EPSILON_SMALL The smallest relative spacing for doubles.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
Complex[]	computeRoots(Complex[] coef) Computes the roots of the polynomial with Complex coefficients.
Complex[]	computeRoots(double[] coef) Computes the roots of the polynomial with real coefficients.
double	getRadius(int index) Returns an a-posteriori absolute error bound on the root.
Complex	getRoot(int index) Returns a zero of the polynomial.
Complex[]	getRoots() Returns the zeros of the polynomial.
boolean	getStatus(int index) Returns the error status of a root.
void	setMaxIterations(int maxIterations) Sets the maximum number of iterations allowed.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

EPSILON_SMALL

public static final double EPSILON_SMALL

The smallest relative spacing for doubles.

See Also:

Constant Field Values

Constructor Detail

ZeroPolynomial

public ZeroPolynomial()

Creates an instance of the solver.

Method Detail

setMaxIterations

public void setMaxIterations(int maxIterations)

Sets the maximum number of iterations allowed. The default value is 30.

Parameters:

maxIterations - an int which specifies the maximum number of iterations allowed

Throws:

IllegalArgumentException - is thrown if maxIterations is less than or equal to zero.

getRoot

public Complex getRoot(int index)

Returns a zero of the polynomial.

Parameters:

index - an int which specifies the (0-based) index of the root to be returned

Returns:

a Complex which represents the index-th root of the polynomial

getRoots

public Complex[] getRoots()

Returns the zeros of the polynomial.

Returns:

a Complex array containing the roots of the polynomial

getRadius

public double getRadius(int index)

Returns an a-posteriori absolute error bound on the root.

Parameters:

index - an int specifying the (0-based) index of the root whose error bound is to be returned

Returns:

a double representing the error bound on the index-th root. NaN is returned if the corresponding root cannot be represented as floating point due to overflow or underflow or if the roots have not yet been computed.

getStatus

public boolean getStatus(int index)

Returns the error status of a root.

Parameters:

index - an int representing the (0-based) index of the root whose error status is to be returned

Returns:

a boolean representing the error status on the index-th root. It is false if the approximation of the index-th root has been carried out successfully, for example, the computed approximation can be viewed as the exact root of a slightly perturbed polynomial. It is true if more iterations are needed for the index-th root.

computeRoots

public Complex[] computeRoots(double[] coef)
                       throws ZeroPolynomial.DidNotConvergeException

Computes the roots of the polynomial with real coefficients.

$$p(x) = {\rm coef}[n] \times x^n + {\rm coef}[n-1] \times x^{n-1} + \ldots + {\rm coef}[0]$$

Parameters:

coef - a double array containing the polynomial coefficients

Returns:

a Complex array containing the roots of the polynomial

Throws:

ZeroPolynomial.DidNotConvergeException

computeRoots

public Complex[] computeRoots(Complex[] coef)
                       throws ZeroPolynomial.DidNotConvergeException

Computes the roots of the polynomial with Complex coefficients.

$$p(x) = {\rm coef}[n] \times x^n + {\rm coef}[n-1] \times x^{n-1} + \ldots + {\rm coef}[0]$$

Parameters:

coef - a Complex array containing the polynomial coefficients.

Returns:

a Complex array containing the roots of the polynomial.

Throws:

ZeroPolynomial.DidNotConvergeException