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

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.