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From Al Chou <>
Subject Re: [math] Greetings from a newcomer (but not to numerics)
Date Mon, 26 May 2003 20:13:11 GMT
--- "J.Pietschmann" <> wrote:
> 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).

Cool.  FYI, _NR_ was first published in FORTRAN 77 and was ported to all other
languages it supports, so it's not the implementation language that matters
when considering _NR_'s license -- you're not even allowed to port their code
to other languages and distribute the ported code without permission.

> 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.

Interesting.  Where's that method from?


Albert Davidson Chou

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