Newton's Root Finding Method for Polynomials.
Finding roots of univariate polynomials.
newtonHorner(p, x0, maxiter = 50, tol = .Machine$double.eps^0.5)
p |
Numeric vector representing a polynomial. |
x0 |
starting value for newtonHorner(). |
maxiter |
maximum number of iterations; default 100. |
tol |
absolute tolerance; default |
Similar to newtonRahson, except that the computation of the
derivative is done through the Horner scheme in parallel with computing
the value of the polynomial. This makes the algorithm significantly
faster.
Return a list with components root, f.root,
the function value at the found root, iter, the number of iterations
done, and root, and the estimated precision estim.prec
The estimated precision is given as the difference to the last solution before stop.
Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.
## Example: x^3 - 6 x^2 + 11 x - 6 with roots 1, 2, 3
p <- c(1, -6, 11, -6)
x0 <- 0
while (length(p) > 1) {
N <- newtonHorner(p, x0)
if (!is.null(N$root)) {
cat("x0 =", N$root, "\n")
p <- N$deflate
} else {
break
}
}
## Try: p <- Poly(c(1:20))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.