newton.clj

(defn newton
   [f fprime tol max-iteration x]
   (if (<= max-iteration 0)
     nil
     (let [y (f x)
           yprime (fprime x)
           x-new (- x (/ y yprime))]
       (if (<= (Math/abs(- x-new x)) (* tol (Math/abs x-new)))
         x-new
         (newton f fprime tol (dec max-iteration) x-new)))))

(newton #(- (* % %) 2) #(* 2 %) 0.00000001 20 100)
;;1.4142135623730951

Line 1: Define function
Line 2: Function arguments. From left to right are:

• f - Function
• fprime - The derivative function of f
• tol - The tolerance
• max-iteration - Maximum number to iterations
• x - The initial position of x

Line 3 - Safe-guarding the recursive function by checking the max-iteration number. If reached max-iteration, return nil.
Line 5 - Bind symbols for the current iteration
Line 8 - The condition to determine whether x-new is closed enough to the solution.
Line 10 - Recursively call newton function with updated x-new and decremented max-iteration.