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Formally certified floating-point filters for homogeneous geometric predicates

Guillaume Melquiond, Sylvain Pion (2007)

RAIRO - Theoretical Informatics and Applications

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 of this...

Formulations Mixtes Augmentées et Applications

Boujemâa Achchab, Abdellatif AGOUZAL (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyse a abstract framework for augmented mixed formulations. We give a priori error estimate in the general case: conforming and nonconforming approximations with or without numerical integration. Finally, a posteriori error estimator is given. An example of stabilized formulation for Stokes problem is analysed.

Fourier analysis of iterative aggregation-disaggregation methods for nearly circulant stochastic matrices

Pultarová, Ivana (2013)

Programs and Algorithms of Numerical Mathematics

We introduce a new way of the analysis of iterative aggregation-disaggregation methods for computing stationary probability distribution vectors of stochastic matrices. This new approach is based on the Fourier transform of the error propagation matrix. Exact formula for its spectrum can be obtained if the stochastic matrix is circulant. Some examples are presented.

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