NUMERICAL FORMULAE. Iteration. Newton Raphson method for refining an
approximate root x0 of f(x)=0 xn+1 = xn − f(xn) f (xn). Particular case to find √N
use ...
NUMERICAL FORMULAE Iteration Newton Raphson method for refining an approximate root x0 of f (x) = 0 xn+1 = xn − Particular case to find Secant Method xn+1 = xn − f (xn )/
f (xn ) f 0 (xn )
√ N use xn+1 =
1 2
f (xn ) − f (xn−1 ) xn − xn−1
xn +
Interpolation
∆fn = fn+1 − fn
,
∇fn = fn − fn−1
,
Gregory Newton Formula
δfn = fn+ 12 − fn− 21 1 µfn = fn+ 12 + fn− 12 2
p(p − 1) 2 p fp = f0 + p∆f0 + ∆ f0 + ... + ∆r f0 2! r where p =