com.numericalmethod.suanshu.analysis.function.polynomial
Class HornerScheme

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.polynomial.HornerScheme

public class HornerScheme
extends java.lang.Object

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

By polynomial remainder theorem,

P(x) = Q(x)(x - x₀) + P(x₀)

That is, it computes the value of a polynomial P(x) at x₀, i.e., P(x₀), and at the same time gives the quotient Q(x).

See Also:

Wikipedia: Horner scheme

Constructor Summary

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

Method Summary

Polynomial	quotient() Get the quotient, the value of P(x).
double	remainder() Get the remainder.

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 at

Method Detail

remainder

public double remainder()

Get the remainder.

Returns:

the remainder

quotient

public Polynomial quotient()

Get the quotient, the value of P(x).

Returns:

the quotient