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ZeroPolynomial Class
The ZeroPolynomial class computes the zeros of a polynomial with complex coefficients, Aberth's method.
Inheritance Hierarchy
SystemObject
  Imsl.MathZeroPolynomial

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
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[SerializableAttribute]
public class ZeroPolynomial

The ZeroPolynomial type exposes the following members.

Constructors
  NameDescription
Public methodZeroPolynomial
Creates an instance of the solver.
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Methods
  NameDescription
Public methodComputeRoots(Double)
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]

Public methodComputeRoots(Complex)
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]

Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetRadius
Returns an a-posteriori absolute error bound on the root.
Public methodGetRoot
Returns a zero of the polynomial.
Public methodGetRoots
Returns the zeros of the polynomial.
Public methodGetStatus
Returns the error status of a root.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyMaximumIterations
The maximum number of iterations allowed.
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Remarks

This class is a 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