Software Demonstration
at the Fifth Workshop on
Computability and Complexity in Analysis
July 12, 2002, Málaga, Spain
As part of the
Fifth Workshop on Computability and Complexity in Analysis
(being a satellite workshop of
ICALP 2002,
the 29th International Colloquium
on Automata, Languages, and Programming)
a demonstration of systems for exact real computation
takes place.
The term exact real computation primarily aims at software packages that
treat (arbitrary) real numbers as atomic objects and that are able to do scientific
computations on these numbers. But this is not meant as an exclusive argument for other packages,
as they provide the algorithmic background.
Aim
The software demonstration is not aiming to be a contest between
different packages. Instead it should allow each of the
participants to demonstrate the strong points and special
abilities of their packages.
In addition to the presentation to the other participants, the intention of
the demonstration is to bring together people working in this field in order
to exchange ideas.
Participants of the Demonstration Session
- MPFR (reliable floating point numbers),
by Vincent Lefevre
- iRRAM (exact reals with an iterative approach),
by Norbert Mueller
- XR (exact reals with an approach using lazy evaluation),
by Keith Briggs
- CORE (robust numerical and geometric computation),
by Chee Yap
Sample Problems
As told above, each package is allowed and even expected to show its strong points.
So the sample problems on the following list are really just samples!
In fact, they are the favorite examples to show the abilities of the
iRRAM-package. ;-)
Of course, important aspects of the demonstration should concern exact real arithmetic (including
approximate algorithms with verified precision, symbolic computation, algebraic methods..., as said before)
- Compute the logistic function
x0=0.5
xn+1=3.75*xn*(1-xn)
for larger values of n,
e.g. give 5 (correct...) decimals of x1000 (=0.79174674...)
Just as a note, the code in the iRRAM package would be:
REAL x = 0.5; REAL c = 3.75;
for ( int i=1; i<=1000; i++ ) x= c*x*(1-x);
rwrite(x,18);
- Compute the inverse of the Hilbert matrix
| 1 |
1/2 |
1/3 |
... |
| 1/2 |
1/3 |
1/4 |
... |
| 1/3 |
1/4 |
1/5 |
... |
| ... |
... |
... |
... |
of size nxn
e.g. with n=100
(either exactly or preferably as an example of inversion of real matrices)
Contact
Norbert Müller (Trier, Germany)
mueller@uni-trier.de
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