Search results for "Mathematical software"
showing 10 items of 60 documents
On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
2018
Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…
Fast Poisson solvers for graphics processing units
2013
Two block cyclic reduction linear system solvers are considered and implemented using the OpenCL framework. The topics of interest include a simplified scalar cyclic reduction tridiagonal system solver and the impact of increasing the radix-number of the algorithm. Both implementations are tested for the Poisson problem in two and three dimensions, using a Nvidia GTX 580 series GPU and double precision floating-point arithmetic. The numerical results indicate up to 6-fold speed increase in the case of the two-dimensional problems and up to 3- fold speed increase in the case of the three-dimensional problems when compared to equivalent CPU implementations run on a Intel Core i7 quad-core CPU…
in Informatique graphique, modélisation géométrique et animation
2007
International audience; no abstract
PROCEDE DE PRE-DISTORSION NUMERIQUE D’UN SIGNAL ET REPETEUR DE TELECOMMUNICATION INTEGRANT UN FILTRE A REPONSE IMPULSIONNELLE FINIE POUR METTRE EN OE…
2013
L'invention concerne un procédé de pré-distorsion numérique d'un signal de télécommunication traité dans un circuit électronique 100 intégrant un filtre à réponse impulsionnelle finie 321. Ce procédé consiste successivement: - à identifier, à la sortie du circuit 100, les paramètres de distorsions de phase et/ou d'amplitude du signal en fonction de la fréquence, - à partir des susdits paramètres de distorsions relevés, à générer, par un algorithme basé sur une interpolation, des coefficients permettant d'effectuer dans ledit filtre 321, des prédistorsions du signal numérique destinées à engendrer une précorrection des susdites distorsions, - à transférer lesdits coefficients de pré-distorsi…
Encouraging students’ problem posing through importing visual images into mathematical software
2017
Tasks and Digital Tools
2016
International audience; This chapter considers scholastic tasks with digital tools. The first two sections consider tasks in ‘ordinary’ classrooms (tasks for learning) and issues relating to tasks using mathematical software. The first section presents examples of tasks with digital tools to highlight potential problems and opportunities for learning. The second section considers issues arising from the literature on tasks design with and without digital tools. The final section looks at task-tool issues in larger-than-the-individual classroom research and in assessment; it also comments of avenues for further development
Mathematical tools in a digital world
2012
There are many vantage points from which to gain a perspective on digital culture. The intersection of mathematics and mathematical tools with all things digital is one such vantage point. This implies an inspection of mathematical software. The broad lines that can be taken are the practice, education and application of mathematics. This thesis focuses on practice and application, disregarding education. With regards the former it is shown how the practice of mathematics itself has been affected by the increasingly pervasive computational nature of our world. From visualisation to theorem proving no area has been untouched. I programmed a subset of the fractal universe, L-Systems, into the…
Comparison of the Root Canal Curvatures of Human Teeth with the Curvatures of the Resin Blocks Used as Models for Training
2019
In this paper we develop a method to associate a function curvature to human teeth roots.These functions are calculated from radiographs using mathematical software. We use this procedure to compare the curvatures of the roots with the curvatures of the resin blocks that are used for learning. The comparison is made by calculating the distances of the corresponding functions in the \(L_1\) metric.
Developing Primary School Students’ Formal Geometric Definitions Knowledge by Connecting Origami and Technology
2019
In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11-12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students’ mathematical knowledge. In previous studies, we developed origami and technology activities for high-school mathematics, but we wanted to explore if such approach would work in primary school as well. For this reason, we chose a flat origami model оf the crane and we used this model to introduce students to basic geometrical notions and definitions, such as points, lines, intersections o…
Limiting Carleman weights and conformally transversally anisotropic manifolds
2020
We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3 3 -manifolds, and 4 4 -manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose …