newton_pseudocode.txt

function newton ( )

Input: f(), fp(), x, xtol, ftol, itmax

it = 0
dx = 0
alpha = 0

Begin loop

  it = it + 1

  Set xold to x, and set x to x - f(x) / fp(x)

  Set dx_old to dx, and set dx = | x - xold |

  Set alpha_old to alpha
  if dx_old is not 0, set alpha to dx / dx_old 
    if alpha_old is not 0, set r = log ( alpha ) / log ( alpha_old )

  if x - xold is less than xtol and |f(x)| is less than ftol, success
  if it > itmax, failure

End loop
  
Output: values of updated x and it