Mathematical Software
In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.
There are many classes of mathematical problems which give rise to matrices, where a large number of the elements are zero. In this case it makes sense to have a special matrix type to handle this class of problems where only the non-zero…
The subject of our talk is the correct evaluation of interval extension of the function specified by the expression x^y without any constraints on the values of x and y. The core of our approach is a decomposition of the graph of x^y into a…
BioSig is an open source software library for biomedical signal processing. Most users in the field are using Matlab; however, significant effort was undertaken to provide compatibility to Octave, too. This effort has been widely…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
This article presents an implementation of a graphical software with various algorithms in Operations research, like minimum path, minimum tree, chinese postman problem and travelling salesman.
ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied…
The solution of large, sparse constrained least-squares problems is a staple in scientific and engineering applications. However, currently available codes for such problems are proprietary or based on MATLAB. We announce a freely available…
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…
Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are…
We give a gentle introduction to using various software tools for automatic differentiation (AD). Ready-to-use examples are discussed, and links to further information are presented. Our target audience includes all those who are looking…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
SnadiOpt is a package that supports the use of the automatic differentiation package ADIFOR with the optimization package Snopt. Snopt is a general-purpose system for solving optimization problems with many variables and constraints. It…
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…
GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More' and Toraldo, this algorithm was designed for large-scale problems but had been…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…