Method 
know 
discretization error 
"roundoff" error 
order/rate 
Taylor expansion  algo 
e_{n} = f^{(n+1)}(ξ) / (n+1)! (xx_{o})^{n+1}


bisection  algo  e_{n} = (ba) / 2^{n} 
 linear 
fixed point  algo  e_{n+1} ≤ K e_{n} , K=Lipschitz constant 
ε / (1−K)  linear 
NewtonRaphson  algo 
e_{n+1} ≤ C e_{n}^{2} 

quadratic 
secant  algo 
e_{n+1} ≤ C e_{n}^{p} , p ≈ 1.62 

p ≈ 1.62 
Müller  idea 
e_{n+1} ≤ C e_{n}^{p} , p ≈ 1.84 

p ≈ 1.84 
inverse quadratic interpolation  idea 
e_{n+1} ≤ C e_{n}^{p} , p ≈ 1.84 

p ≈ 1.84 
polynomial interpolation  algo 
e_{N} = f^{(N+1)}(ξ) /(N+1)! ∏_{i=0}^{N}(xx_{i}) 
½(2^{N}+1) ε  
piecewise interpolation  idea 

Hermite  idea  
spline  idea  
Bezier curve  idea  
forward FD for f′(x)  algo 
O(h)  ε / h 
1st order 
backward FD for f'(x)  algo 
O(h)  ε / h 
1st order 
centered FD for f'(x)  algo 
O(h^{2})  ε / h 
2nd order 