dev.nm.analysis.function.polynomial

Class HornerScheme

java.lang.Object

dev.nm.analysis.function.polynomial.HornerScheme

public class HornerScheme
extends Object

Horner scheme is an algorithm for the efficient evaluation of polynomials in monomial form. It can also be seen as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule.

The polynomial remainder theorem says:

 P(x) = Q(x)(x - x0) + P(x0)
 

We thus can compute the value of a polynomial P(x) at \(x_{0}\), i.e., \(P(x_{0})\), and at the same time the quotient Q(x).

See Also:

Wikipedia: Horner scheme

Constructor Summary

Constructors

Constructor and Description
HornerScheme(Polynomial polynomial, double x) Evaluate a polynomial at x.

Method Summary

Modifier and Type	Method and Description
Polynomial	quotient() Get the quotient, Q(x).
double	remainder() Get the remainder, \(P(x_{0})\).

Methods inherited from class java.lang.Object

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

Constructor Detail

HornerScheme

public HornerScheme(Polynomial polynomial,
                    double x)

Evaluate a polynomial at x.

Parameters:

polynomial - a polynomial

x - a point to evaluate the polynomial at

Method Detail

remainder

public double remainder()

Get the remainder, \(P(x_{0})\).

Returns:

the remainder

quotient

public Polynomial quotient()

Get the quotient, Q(x).

Returns:

the quotient