Re: [HM] First iteration use

Snow, Donald R. (snowd@math.byu.edu)
Mon, 14 Sep 1998 18:58:38 -0600

If the idea of iterations begins with solving nonlinear equations, then
shouldn't the Babylonians (2000 BC) be considered to be the first to do
iterations? Their square-root method of averaging an approximation and its
reciprocal, which are above and below the exact value, is equivalent to
Newton's method applied to solving f(x) = x^2 - a.

Don Snow

At 07:36 PM 9/14/98 +0200, Robert Erra wrote:

>Hello,
>
>the history of "iterations" begins certainly with the history of numerical
>methods for solving a nonlinear equation.
>
>For example, I've read in a French book that Newton has not explicitly proposed
>such an iteration with the method that is now called "Newton-Raphson-Simpson
>method ".
>Newton (circa 1669) and Raphson (circa 1690) has proposed the algorithm/method
>for polynomial equations with rational coefficients, Simpson has proposed the
>algortihm for irrational and transcendental equations (circa 1740).
>The book has been translated in English (it has a lot of original texts):
>J.-L. Chabert "A history of algorithm" Springer 1998, ISBN 3-540-63369-3.
>You will find also classical references about history of False Position
>methods and Square roots computations.

Dr. Donald R. Snow, Dept of Mathematics, Brigham Young University, Provo,
Utah 84602, (801) 378-2366, snowd@math.byu.edu