newton

Builtin index · Signal processing

result = newton(f, fprime, x0, [tol=1e-12], [max_iter=100])

Input: f, fprime, x0, tol, max_iter · Output: result

What it is

f, fprime: strings naming user-defined functions of one number (the function and its derivative); x0: number, the starting guess; tol/max_iter (optional numbers).

Overloads

One call shape — this function is not overloaded.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

f(x) := x^2 - 2
root = fzero("f", 0, 2)          # Brent's method: needs a bracket

                                   # [a,b] where f changes sign, always

                                   # converges, no derivative needed


fprime(x) := 2*x
root2 = newton("f", "fprime", 1.0)  # Newton's method: fast (quadratic

                                      # convergence) when it works, but

                                      # needs a derivative and can diverge

from numerics-dsp

How it works

newton(f, fprime, x0, [tol=1e-12], [max_iter=100]) — Newton's method: fast (quadratic convergence) when it works, but needs a derivative and can diverge from a poor starting guess, unlike fzero.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.