The standard diffusion curve used in models of TAP reactors, as it is usually defined, is numerically unstable for small values. We use a functional equation satisfied by the curve to define a numerically stable way of computing it for all values.
SymJAX is a symbolic programming version of JAX simplifying graph input/output/updates and providing additional functionalities for general machine learning and deep learning applications. From an user perspective SymJAX provides a la Theano experience with fast graph optimization/compilation and broad hardware support, along with Lasagne-like deep learning functionalities.
We present the Mathematical Functions Grimoire (FunGrim), a website and database of formulas and theorems for special functions. We also discuss the symbolic computation library used as the backend and main development tool for FunGrim, and the Grim formula language used in these projects to represent mathematical content semantically.
Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\ldots,a_n)$ where the extensions numbers $a_k$ may be algebraic or transcendental. The system combines efficient field operations with automatic discovery and certification of algebraic relations, resulting in a practical computational model of $\mathbb{R}$ and $\mathbb{C}$ in which equality is rigorously decidable for a large class of numbers.
We present the Alsvinn simulator, a fast multi general purpose graphical processing unit (GPGPU) finite volume solver for hyperbolic conservation laws in multiple space dimensions. Alsvinn has native support for uncertainty quantifications, and exhibits excellent scaling on top tier compute clusters.
Xorshift128+ is a newly proposed pseudorandom number generator (PRNG), which is now the standard PRNG on a number of platforms. We demonstrate that three-dimensional plots of the random points generated by the generator have visible structures: they concentrate on particular planes in the cube. We provide a mathematical analysis of this phenomenon.
In the article we outline the set of Matlab functions that enable the computation of elliptic Integrals and Jacobian elliptic functions for real arguments. Correctness, robustness, efficiency and accuracy of the functions are discussed in some details. An example from the elasticity theory illustrates use of the collection.
This short paper briefly describes the implementation of the least squares Monte Carlo method in the rlsm package. This package provides users with an easy manner to experiment with the large amount of R regression tools on any regression basis and reward functions. This package also computes lower and upper bounds for the true value function via duality methods.
In article the basic principles put in a basis of algorithmicallysoftware of hypercomplex number calculations, structure of a software, structure of functional subsystems are considered. The most important procedures included in subsystems are considered, program listings and examples of their application are given.
We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, Pólya theory, combinatorial species, and asymptotics. We describe the capabilities that the packages offer as well as some of the algorithms used, and provide links to original documentation. Most of the packages are freely downloadable from the web.
The mean and variance of the number of appearances of a given subgraph $H$ in an Erdős--Rényi random graph over $n$ nodes are rational polynomials in $n$. We present a piece of software named Polcovar (from "polynomial" and "covariance") that computes the exact rational coefficients of these polynomials in function of $H$.
Over the past decade, the high performance computing community has become increasingly concerned that preserving the reliable, digital machine model will become too costly or infeasible. In this paper we discuss four approaches for developing new algorithms that are resilient to hard and soft failures.
In this paper we describe how DUNE, an open source scientific software framework, is developed. Having a sustainable software framework for the solution of partial differential equations is the main driver of DUNE's development. We take a look how DUNE strives to stay sustainable software.
We give a link to a page on the Web on which we deposited a set of eight huge Linear Programming (LP) problems for Intensity-Modulated Proton Therapy (IMPT) treatment planning. These huge LP problems were employed in our recent research and we were asked to make them public.
The present study represents "The Fislab package of programs meant to develop the fuzzy regulators in the Scilab environment" in which we present some general issues, usage requirements and the working mode of the Fislab environment. In the second part of the article some features of the Scilab functions from the Fislab package are described.
This paper presents an algorithm for computing Sine-Cosine pairs to modest accuracy, but in a manner which contains no conditional tests or branching, making it highly amenable to vectorization. An exemplary implementation for PowerPC AltiVec processors is included, but the algorithm should be easily portable to other achitectures, such as Intel SSE.
We propose performance profiles-distribution functions for a performance metric-as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.