Re: Zero finding function, solving
From: Dr John Stockton (spam_at_merlyn.demon.co.uk)
Date: 11/25/03
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Date: Tue, 25 Nov 2003 11:58:09 +0000
JRS: In article <3fc2616a$1@newsgroups.borland.com>, seen in news:borla
nd.public.delphi.language.objectpascal, John Herbster (TeamB) <herb-
sci1_AT_sbcglobal.net@?.?> posted at Mon, 24 Nov 2003 13:52:55 :-
>
>"RTI" <Rigas@Caaisn.leeds.ac.uk> wrote
>> The solution has to be very accurate up to e-15. It is all about
>> determining Earth's eccentricity.
>
>I think that the Earth's radius is about 6437376 meters or
>about 1.17E13 wavelengths of green light, so your 1E15
>accuracy could represent the radius of the Earth to about
>1/100 of one wavelength of green light. Of course if your
>calulations are "ill formed" then you may need more accurate
>trig functions. Maybe this is a case for type extended. --JohnH
Eccentricity probably refers to the shape of the Earth's orbit, not to
the shape of the Earth which is more likely to be ellipticity or
oblateness or some word which I have forgotten.
In such calculations, numerical errors tend to build up a lot; and
subtractions of similar quantities may in practice be unavoidable.
Extended should certainly be used in much of the calculation; any
slowness caused by it having more bytes should be easily out-compensated
by better and/or fewer iterations.
Newton's method requires the ability to differentiate the function;
<URL:http://www.merlyn.demon.co.uk/js-demos.htm#FZ> demonstrates
solution by binary-chop, using javascript.
-- © John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v4.00 IE 4 © <URL:http://jibbering.com/faq/> Jim Ley's FAQ for news:comp.lang.javascript <URL:http://www.merlyn.demon.co.uk/js-index.htm> JS maths, dates, sources. <URL:http://www.merlyn.demon.co.uk/> TP/BP/Delphi/JS/&c., FAQ topics, links.
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