Displaying similar documents to “Algorithms for the inclusion of solutions of ordinary initial value problems”

Extension of the C-XSC Library with Scalar Products with Selectable Accuracy

Zimmer, Michael, Krämer, Walter, Bohlender, Gerd, Hofschuster, Werner (2010)

Serdica Journal of Computing

Similarity:

The C++ class library C-XSC for scientific computing has been extended with the possibility to compute scalar products with selectable accuracy in version 2.3.0. In previous versions, scalar products have always been computed exactly with the help of the so-called long accumulator. Additionally, optimized floating point computation of matrix and vector operations using BLAS-routines are added in C-XSC version 2.4.0. In this article the algorithms used and their implementations, as well...

Formally certified floating-point filters for homogeneous geometric predicates

Guillaume Melquiond, Sylvain Pion (2007)

RAIRO - Theoretical Informatics and Applications

Similarity:

Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification...