Mixed volumes of lattice polytopes play a central role in numerical and tropical algebraic geometry. We present an implementation of a new algorithm for their computation based on tropical homotopy continuation, which is a combinatorial procedure using ideas from numerical algebraic geometry. While the mathematical aspects of the algorithm are presented elsewhere, here we mainly address technic...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

in this paper, the researchers present a multi-objective linear fractional inventory model using fuzzy pro-gramming. the proposed method in this paper is applied to a problem with two objective functions. the re-sulted fuzzy model is transformed into an ordinary linear programming. the implementation of the develop-ing model presented in this paper is demonstrated through the use of some numeri...

In this paper, a theoretical background is presented for the stabilisation of non-linear systems. A numerical implementation is then proposed. The class of systems concerned with the. proposed practical approach is quite large and contains all flat systems as a particular subset. The stabilising strategy is based on path generation strategy and avoids the integration of the differential system....

Information in newspapers is often showed in the form of numerical expressions which present comprehension problems for many people, including people with disabilities, illiteracy or lack of access to advanced technology. The purpose of this paper is to motivate, describe, and demonstrate a rule-based lexical component that simplifies numerical expressions in Spanish texts. We propose an approa...

The BLAS library is one of the central libraries for the implementation of numerical algorithms. It serves as the basis for many other numerical libraries like LAPACK, PLASMA or MAGMA (to mention only the most obvious). Thus a fast BLAS implementation is the key ingredient for efficient applications in this area. However, for debugging or benchmarking purposes it is often necessary to replace t...

The numerical solution of two-layer shallow water systems is required to simulate accurately stratified fluids, which are ubiquitous in nature: they appear in atmospheric flows, ocean currents, oil spills, . . .Moreover, the implementation of the numerical schemes to solve these models in realistic scenarios imposes huge demands of computing power. In this paper, we tackle the acceleration of t...

This contribution presents a VHDL-AMS implementation of a novel numerical carbon nanotube transistor (CNT) modelling approach which relies on a flexible and efficient cubic spline non-linear approximation of the non-equilibrium mobile charge density. The underlying algorithm creates a rapid and accurate solution of the numerical relationship between the charge density and the self-consistent vo...