edu.northwestern.at.utils.math
Class Polynomial

java.lang.Object
  edu.northwestern.at.utils.math.Polynomial

public class Polynomial
extends java.lang.Object

Polynomial functions.

Constructor Summary

protected

Polynomial() Don't allow instantiation but do allow overrides.

Method Summary

static double	evaluateChebyschev(double[] coeffs, double x) Evaluates a Chebyschev series.
static double	hornersMethod(double[] polycoefs, double x) Evaluate a polynomial expression using Horner's method.

Methods inherited from class java.lang.Object

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

Constructor Detail

Polynomial

protected Polynomial()

Don't allow instantiation but do allow overrides.

Method Detail

hornersMethod

public static double hornersMethod(double[] polycoefs,
                                   double x)

Evaluate a polynomial expression using Horner's method.

Parameters:

polycoefs - Array of polynomial coefficients. The coefficients should be ordered with the constant term first and the coefficient for the highest powered term last.

x - Value for which to evaluate polynomial.

Returns:

Polynomial evaluated using Horner's method.

Horner's method is given by the following recurrence relation: c[i]*x^i + ... + c[1]*x + c[0] = c[0] + x*(c[i-1]*x^[i-1] + ... + c[1])

Horner's method avoids loss of precision which can occur when the higher-power values of x are computed directly.

evaluateChebyschev

public static double evaluateChebyschev(double[] coeffs,
                                        double x)

Evaluates a Chebyschev series.

Parameters:

coeffs - The Chebyschev polynomial coefficients.

x - The value for which to evaluate the polynomial.

Returns:

The Chebyschev polynomial evaluated at x.