newton <- function ( f, fp, x, tol = 1.0e-3, m = 100 )

#*****************************************************************************80
#
## newton seeks the root of a function using Newton's method.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    13 March 2020
#
#  Author:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  iter <- 0
  oldx <- x + 10.0 * tol

  while ( tol < abs ( x - oldx ) )
  {
    iter <- iter + 1
    if ( m < iter )
    {
      warning ( 'newton: iteration limit exceeded.' )
      break
    }

    oldx <- x
    x <- x - f ( x ) / fp ( x )
  }

  return ( x )
}