pracma (version 0.2-2)

horner: Horner's Method

Description

Compute the value of a polynomial via the Horner scheme.

Usage

horner(p, x)

Arguments

p

Numeric vector representing a polynomial.

x

Numeric scalar or vector at which to evaluate the polynomial.

Value

• Returns a list with two elements, list(y=..., dy=...) where the first list elements returns the values of the polynomial, the second the values of its derivative at the point(s) x.

Details

Utilizes the Horner scheme to evaluate the polynomial and its first derivative at the same time.

The polynomial p = p_1*x^n + p_2*x^{n-1} + ... + p_n*x + p_{n+1} is hereby represented by the vector p_1, p_2, ..., p_n, p_{n+1}, i.e. from highest to lowest coefficient.

References

Quarteroni, A., and Saleri, F. (2006) Scientific Computing with Matlab and Octave. Second Edition, Springer-Verlag, Berlin Heidelberg.

See Also

polyval

Examples

x <- c(-2, -1, 0, 1, 2)
p <- c(1, 0, 1)  # polynomial x^2 + x, derivative 2*x
horner(p, x)$y   #=>  5  2  1  2  5
horner(p, x)$dy  #=> -4 -2  0  2  4