Newton-Raphson method

newton_rahpson.coffee

newton_raphson = (f, x0)->
  x0 = Math.random() if typeof x0 isnt "number"
  fx0 = f(x0)
  x = x0 + 0.01 # for approximating gradient
  loop
    fx = f(x)
    gradient = (fx - fx0) / (x - x0)
    delta = fx/gradient
    break if Math.abs(delta) < 0.0000001
    x0 = x
    fx0 = fx
    x = x - delta

  return x

# sample x^2 + 3x - 2 = 0 : (x-1)(x-2) = 0
console.log newton_raphson (x)->
  return Math.pow(x,2) - 3*x + 2