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Number representation - Juergen Rodenkirchen - 02-24-2008

Hi all!

Does any one of you know a source (book, internet) that deals with the effect of number representations on the solving of (linear) systems of equations? Thanks for your input in advance.

Juergen


Re: Number representation - Mad Dog ebaycalcnut - 02-24-2008

I assume you have done some google searches. Doing this, I got some interesting results.

I entered the following keywords into google:

number representations linear systems

To be honest, I don't know much about number representations. My expertise is different.


Re: Number representation - Juergen Rodenkirchen - 02-24-2008

Thanks for your input anyway :-)

Regards, Juergen


Re: Number representation - John Ferman - 02-24-2008

Juergen, could you elaborate on what you mean by number representations. The first things that come into my mind are decimal or exponential. In solving linear equations, both matrix and vector operations come into play; first matrix inversion, then matrix vector multiplication. I am guessing your query has to do with overflow/underflow in the number storage locations. I don't remember seeing any books that cover those kind of issues.


Re: Number representation - Juergen Rodenkirchen - 02-25-2008

Hi John!

Well, sort of that. I'm looking for a way of estimating the error of a Gauss-Elimination say (exact algorithm), depending on the base and mantissa-width of the floating point numbers used or the like ...

Regards,
Juergen


Re: Number representation - Patrice Guérin - 02-27-2008

Hi Juergen,

When I was at the university in the 80's, my course in Numerical
Analysis was teached by Jean Vignes.
He was the author of a book about "La méthode PEPER"
(method of permutation-perturbation) to estimate the error
of numerical methods when some error are introduced on the
last significant digit of a number.
I know that the book exist in french, and maybe
I always have documents about this.

Here are some links I've found (mostly in french, sorry)

http://www.editionstechnip.com/sources/Liste_Fiche.asp?CV=151.001
http://books.google.fr/books?id=gkfHlYIV300C&pg=PA253&lpg=PA253&dq=m%C3%A9thode+peper&source=web&ots=D3uJb82As5&sig=xr3ZcKvCKhbR3KWwfqisB8dioJU&hl=fr
http://www.springerlink.com/content/v02gjun47l058564/
http://www.lip6.fr/Laboratoire/Rapport_2000/ANP.pdf See page 9 of pdf file, referring to CADNA and CESTAC.
Hope this helps