Package 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:

  • Field Details

    • EPSILON_SMALL

      public static final double EPSILON_SMALL
      The smallest relative spacing for doubles.
      See Also:

  • Constructor Details

    • ZeroPolynomial

      public ZeroPolynomial()
      Creates an instance of the solver.

  • Method Details

    • 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