Newton Raphson Solver

newtonraphson.lua

local DOUBLE_IEEE_ACCURACY = 1e-8

local function areFuzzyEqual(a, b, accuracy)
  return (math.abs(a-b) < (accuracy or DOUBLE_IEEE_ACCURACY))
end

local function derivative(f, x0, accuracy)
  local h = 0.1
  local xL, xR = x0 - h, x0 + h
  local tAccr = (f(xR) - f(xL))/(2*h)

  repeat
    local tAccr2 = tAccr
    h = h/2
    xL, xR = x0 - h, x0 + h
    tAccr = (f(xR) - f(xL))/(2*h)
  until areFuzzyEqual(tAccr, tAccr2, accuracy)

  return tAccr
end

local function newtonRaphsonSolver(f, x0, accuracy)
  local xi, xi_1
  
  repeat
    xi_1 = xi
    xi = xi - (f(x0)/derivative(f, x0))
  until areFuzzyEqual(xi, xi_1, accuracy)
  
  return xi
end