Related papers: LSJK - a C++ library for arbitrary-precision numer…

Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…

Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…

We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating functions of polylogarithms to integrals involving the sine…

Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…

We give an introduction to the C++ library GiNaC, which extends the C++ language by new objects and methods for the representation and manipulation of arbitrary symbolic expressions.

We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this…

A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…

Effective is a C++ library which provides the user a toolbox to study the effective action of an arbitrary field theory. From the field content, gauge groups and representations an appropriate action is generated symbolically. The effective…

In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future…

The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many…

We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the…

This article is about twofold arithmetic. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function $y_0+y_1 \approx f(x_0+x_1)$ is nearly…

We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…

We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes use of the well-known observation that although the Bessel…

A C++ class was written for the calculation of frequentist confidence intervals using the profile likelihood method. Seven combinations of Binomial, Gaussian, Poissonian and Binomial uncertainties are implemented. The package provides…

This paper introduces LSEMINK, an effective modified Newton-Krylov algorithm geared toward minimizing the log-sum-exp function for a linear model. Problems of this kind arise commonly, for example, in geometric programming and multinomial…

We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…

We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering…