Newton-Raphson Method

• Can one do better than linear convergence? Duh!

• Expand f(x) in a Taylor series:

  • f(x + ) = f(x) + f '(x)  + f "(x) 2/2 + ...

• For  << x, drop higher order terms, so:

  • f(x + ) = 0   = - f(x) / f '(x)

•  is correction added to current guess of root:

  • i.e. xi+1 = xi + 

Notes: