Re: Secant method vs Newton's method

On Thu, 21 Sep 2006 22:29:08 +0100, Schizoid Man <schiz@xxxxxx> wrote:

Hi,

Under what circumstances would I prefer the secant method to Newton's
method?

Newton's method converges much faster and the number of function calls
seem to be the same (if we assume the derivative is a function call).

This isn't quite right. The convergence rate for the secant method is
~1.6 for one function evaluation and ~2.6 for two. Newton's method is
~2 for one function evaluation and one derivative evaluation. If
function evaluations and derivative evaluations are equally costly the
secant method is faster. If derivative evaluations are cheap the
Newton method is faster. Also, the Newton method has better numerical
properties.



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