Search results for "Numerical Analysis"
showing 3 items of 883 documents
The Tucker tensor decomposition for data analysis: capabilities and advantages
2022
Tensors are powerful multi-dimensional mathematical objects, that easily embed various data models such as relational, graph, time series, etc. Furthermore, tensor decomposition operators are of great utility to reveal hidden patterns and complex relationships in data. In this article, we propose to study the analytical capabilities of the Tucker decomposition, as well as the differences brought by its major algorithms. We demonstrate these differences through practical examples on several datasets having a ground truth. It is a preliminary work to add the Tucker decomposition to the Tensor Data Model, a model aiming to make tensors data-centric, and to optimize operators in order to enable…
Reliable Outer Bounds for the Dual Simplex Algorithm with Interval Right-hand Side
2013
International audience; In this article, we describe the reliable computation of outer bounds for linear programming problems occuring in linear relaxations derived from the Bernstein polynomials. The computation uses interval arithmetic for the Gauss-Jordan pivot steps on a simplex tableau. The resulting errors are stored as interval right hand sides. Additionally, we show how to generate a start basis for the linear programs of this type. We give details of the implementation using OpenMP and comment on numerical experiments.
Strain hardening in liquid-particle suspensions
2005
The behavior of a liquid-particle suspension induced to sheared motion was analyzed by numerical simulations. When the velocity (strain) of the suspension began to increase, its viscosity first stayed almost constant, but increased then rapidly to a clearly higher level. This increase in viscosity is shown to be related to formation of clusters of suspended particles. Clusters are shown to increase the viscosity by enhanced momentum transfer though clustered particles. This is the mechanism behind the strain-hardening phenomenon observed in small-strain experiments on liquid-particle suspensions.