From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Re: Dekker's algorithm
Date: 16 Jun 1998 16:26:27 GMT

In article <lkoene-ya02408000R1506982116520001@news.worldonline.nl>,
 lkoene@NO-SPAM.worldonline.nl (L. Koene) writes:
|> A method for interpolation is Dekker's algorithm.
|> It is said to be useful for finding zeros of arbitrary
|> real functions f(x).
|> 
|> How does the  algorithm work? And how effective is it 
|> compared with other numerical methods for  determining 
|> roots?

this is an algorithm which combines inverse quadratic interpolation, linear
interpolation and bisection in order to obtain fast global and fast local
convergence. It has root-order 1.839 asymptotically, yet needs only
one fresh function evaluation and no derivative values of course,
is therefore mor efficient than the pure secant method and newtons method of
course, but slower than newton. in forsythe-malcolm-moler
"computer methods for mathematical computations",
prentice hall publ. 1977  there is a nice description plus
fortran source, also available from netlib, library fmm.
hope this helps
peter