Derivatives on HP 42S

[Albert Chan]

A blog from the inventor of Complex Step Differentiation Algorithm.
It had a fully worked out example, showing very stable and accurate estimates:

https://blogs.mathworks.com/cleve/2013/1...entiation/

Real part of f(x + h*I) is also useful, for getting second derivative (involve subtraction):

http://ancs.eng.buffalo.edu/pdf/ancs_pap..._gnc06.pdf

Since we already have the value of y = f(x + h*I) of approximate extremum x, we can improve it:

Code:

from cmath import *
f = lambda x: sin(x) ** exp(x)  # rework post 3
x, h = 14.137167, 1e-6          # try to improve extremum x
y = f(complex(x, h))

# Newton's method, using f''(x) = 2/(h*h) * (f(x).real - y.real)
x -= h/2 * y.imag / (f(x).real - y.real)

2nd order x = 14.137167
3rd order x = 14.1371669412
    Actual x = 14.137166942003920 ...