From: Nuralanur@...
Date: 2006-08-08T17:58:03+09:00
Subject: Re: Profiling Ruby Matrix operations

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>> This is the sort of code I'd *like* to write in pure Ruby, rather  than
>> having to call a C library for efficiency. The matrix I  generated is
>> quite ill-conditioned. It's quite possible that a  "standard" floating
>> point numerical determinant or matrix inversion  routine would choke on
>> it, while the combination of "matrix",  "mathn" and "rational" I used
>> had no problem with it. In short, I'm  willing to pay for rational
>> arithmetic and correct results, but not  for an inefficient
>> interpreter. :) So if someone is going to rewrite  Matrix in C, they
>> need to do the underlying arithmetic  too.
>>     

There are some theoretical considerations about exact arithmetic,  made
processor-effiicient, in two papers:
 
E. Kaltofen and V. Pan. 
Processor efficient parallel solution  of linear systems over an abstract 
field. 
In Proc. SPAA '91 3rd Ann. ACM  Symp. Parallel Algor. Architecture, pages 
180-191, New York, N.Y., 1991.  ACM Press
 
E. Kaltofen and V. Pan. 
Processor-efficient parallel solution  of linear systems II: the positive 
characteristic and singular cases. 
In  Proc. 33rd Annual Symp. Foundations of Comp. Sci., pages 714-723, Los  
Alamitos, California, 1992. IEEE Computer Society Press. 

These can be downloaded from 
_http://www4.ncsu.edu/~kaltofen/bibliography/index.html#SECTION00022000000000000000_ 
(http://www4.ncsu.edu/~kaltofen/bibliography/index.html#SECTION00022000000000000000) 
 
From the website, it looks as if these algorithms were implemented in  
LINBOX: a generic library for exact  black box linear algebra. The homepage 
including downloads can be found  at _www.linalg.org_ (http://www.linalg.org/) . 
 
Best regards,
 
Axel
 
 
 

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