The Museum of HP Calculators

HP Forum Archive 18

 Number representationMessage #1 Posted by Juergen Rodenkirchen on 24 Feb 2008, 3:45 a.m. 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 representationMessage #2 Posted by Mad Dog ebaycalcnut on 24 Feb 2008, 2:46 p.m.,in response to message #1 by Juergen Rodenkirchen 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 representationMessage #3 Posted by Juergen Rodenkirchen on 24 Feb 2008, 4:33 p.m.,in response to message #2 by Mad Dog ebaycalcnut Thanks for your input anyway :-) Regards, Juergen

 Re: Number representationMessage #4 Posted by John Ferman on 24 Feb 2008, 6:03 p.m.,in response to message #1 by Juergen Rodenkirchen 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 representationMessage #5 Posted by Juergen Rodenkirchen on 25 Feb 2008, 4:17 p.m.,in response to message #4 by John Ferman 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 representationMessage #6 Posted by Patrice Guérin on 27 Feb 2008, 8:13 p.m.,in response to message #5 by Juergen Rodenkirchen 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

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