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From "J.Pietschmann" <>
Subject Re: [math] Greetings from a newcomer (but not to numerics)
Date Mon, 26 May 2003 19:53:37 GMT
Al Chou wrote:
> The best derivative-less algorithm I know of is the van Wijngaarden - Dekker -
> Brent method described in _NR_.  I have been pondering lately the issue of
> implementing algorithms that I know of from _NR_ without violating their
> license, which explicitly restricts redistribution of source code based on
> their published code.  But I don't know whether a clean-room implementation is
> worth the time or likely to be as good as a published implementation.  Any
> thoughts from out there?

I can supply an implementation based on H.M.Antia: "Numerical
Methods for Scientists and Engineers" which does not have such
a restriction (the sample code is FORTRAN, anyway).

Then there is a method which uses quadratic interpolation (instead
of inverse quadratic interpolation as Brent), which requires
solving a quadratic but is still performant if square roots
are cheap (and they are in modern hardware, of the same order as
a FP division). The method is still derivative-less but should
converge quadratically (same as Newton) as long as the function
has a smooth second order derivative. I've never seen this analyzed
in a textbook though.


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