Demonstration of the Secant method (Sekantenmethode) with an initial Newton step.

sekanten.coffee

# functions
f = (x) ->
	2 - x*x - Math.exp(x)

fd = (x) ->
	-2*x - Math.exp(x)

newt = (x) ->
	x - f x / fd x

sek = (xp, x) ->
	x - (x - xp) / ( f x - f xp ) * f x

log = (i,s) ->
	console.log i + ': ' + s

# go!
xp = 2.5;
log 0,xp

# one newton step
x = newt xp
log 1,x

# 7 secant steps
for i in [2..8]
	oldx = x
	x = sek xp,x
	xp = oldx
	log i,x