Package dev.nm.analysis.function.polynomial

Class CauchyPolynomial

java.lang.Object

dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

dev.nm.analysis.function.polynomial.Polynomial

dev.nm.analysis.function.polynomial.CauchyPolynomial

All Implemented Interfaces:

AbelianGroup<Polynomial>, Monoid<Polynomial>, Ring<Polynomial>, VectorSpace<Polynomial,Real>, Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class CauchyPolynomial
extends Polynomial

The Cauchy's polynomial of a polynomial takes this form:

 C(x) = |p_n|x^n + |p_{n-1}|x^{n-1} + ... + |p_1|x - |p_0| = 0
 

Note: the sign of the constant is negative.

Nested Class Summary

Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException

Field Summary

Fields inherited from class dev.nm.analysis.function.polynomial.Polynomial

ONE, ZERO

Constructor Summary

Constructors

Constructor	Description
CauchyPolynomial(Polynomial p)

Method Summary

Modifier and Type	Method	Description
double	lowerBound()	Cauchy's lower bound on polynomial zeros is the unique positive root of the Cauchy polynomial.

Methods inherited from class dev.nm.analysis.function.polynomial.Polynomial

add, degree, equals, evaluate, evaluate, evaluate, getCoefficient, getCoefficients, getNormalization, hashCode, minus, multiply, ONE, opposite, pow, scaled, scaled, toString, ZERO

Methods inherited from class dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dimensionOfDomain, dimensionOfRange

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface dev.nm.analysis.function.Function

dimensionOfDomain, dimensionOfRange

Constructor Details

CauchyPolynomial

public CauchyPolynomial(Polynomial p)

Method Details

lowerBound

public double lowerBound()

Cauchy's lower bound on polynomial zeros is the unique positive root of the Cauchy polynomial.

Returns:

Cauchy's lower bound