Extending the Range of C-XSC: Some Tools and Applications for the use in Parallel and other Environments

Abstract

There is a broad range of packages and libraries for verified numerical
computation. C-XSC is a library combining one of the most extensive
sets of functions and operations on the one hand with a wide range of
applications and special features on the other hand. As such it is an
important task both to make use of its existing capabilities in applications
and to develop further extensions giving access to additional areas and
environments.
In this talk, we present some examples of extensions for C-XSC that
have been developed lately. Among these are extensions that give access
to further hardware and software environments as well as applications
making use of these possibilities.
Software libraries for interval computation always imply great computation
effort: One way to reduce computation times is the development
of parallel methods to make use of parallel hardware. For this, it is important
that the features and data types of the used library can be easily
used in parallel programs. An MPI package for C-XSC data types allows
to easily use C-XSC in parallel programs without bothering about the internal
structure of data types. Another extension of C-XSC, the C-XSC
Taylor arithmetic, is also covered by the MPI package. Parallel verified
linear system solvers based on the package are available as well, and further
development has been and is being done to integrate more efficient
methods for interval linear system solution.
One application making use of the mentioned extensions is a parallel
verified Fredholm integral equation solver. Some results are given to
demonstrate the reduction of computation time and, at the same time,
the accuracy gain that can be obtained using the increased computation
power. Naturally, hardware interval support would offer still more
possibilities towards optimal performance of verified numerical software.
Another possibility to extend the range of C-XSC is to make results
available for further computations in other software environments as,
for example, computer algebra packages. An example of this is presented
for the Maple interval package intpakX. This kind of interfaces also
allows the user to get access to further platforms like operating systems,
compilers or even hardware.

References:
[1] ALiCEnext: http://www.alicenext.uni-wuppertal.de.
[2] Blomquist, F.; Hofschuster, W.; Kraemer, W.: Real and Complex Taylor
Arithmetic in C-XSC. Preprint BUW-WRSWT 2005/4, University of
Wuppertal, 2005.
[3] Grimmer, M.; Kraemer, W.: An MPI Extension for Verified Numerical Computations
in Parallel Environments. In: Int. Conf. on Scientific Computing
(CSC’07, Worldcomp’07) Las Vegas, June 25-28, 2007, Proceedings
pp. 111-117, Arabnia et al. (eds.), 2007.
[4] Grimmer, M.: An MPI Extension for the Use of C-XSC in Parallel Environments.
Preprint BUW-WRSWT 2005/3, University of Wuppertal,
2005.
[5] Grimmer, M.: Selbstverifizierende mathematische Softwarewerkzeuge im
High Performance Computing. Dissertation, Logos Verlag, Berlin, 2007.
[6] Grimmer, M.: Interval Arithmetic in Maple with intpakX. In: PAMM -
Proceedings in Applied Mathematics and Mechanics, Vol. 2, Nr. 1, p.
442-443, Wiley-InterScience, 2003.
[7] Hofschuster, W.; Kraemer, W.: C-XSC 2.0: A C++ Library for Extended
Scientific Computing. Numerical Software with Result Verification, Lecture
Notes in Computer Science, Volume 2991/2004, Springer-Verlag, Heidelberg,
pp. 15 - 35, 2004.
[8] Klein, W.: Enclosure Methods for Linear and Nonlinear Systems of Fredholm
Integral Equations of the Second Kind. In: Adams, Kulisch: Scientific
Computing with Result Verification, Academic Press, 1993.