Related papers: Sample programs in C++ for matrix computations in …
Pipelined algorithms implemented in field programmable gate arrays are being extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms are increases rapidly. For…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
Several ways to accelerate the solution of 2D/3D linear min-max problems in $n$ constraints are discussed. We also present an algorithm for solving such problems in the 2D case, which is superior to CGAL's linear programming solver, both in…
We present f4ncgb, a new open-source C++ library for Gr\"obner basis computations in free algebras, which transfers recent advancements in commutative Gr\"obner basis software to the noncommutative setting. As our experiments show, f4ncgb…
The article highlights the promising ways of providing access to the mathematical software in higher educational institutions. It is emphasized that the cloud computing services implementation is the actual trend of modern ICT pedagogical…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
Currently, multi/many-core CPUs are considered standard in most types of computers including, mobile phones, PCs or supercomputers. However, the parallelization of applications as well as refactoring/design of applications for efficient…
This paper explores the relationship between C++ templates and partial evaluation. Templates were designed to support generic programming, but unintentionally provided the ability to perform compile-time computations and code generation.…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
I will present my implementation 'n-units' of physical units into C++ programs. It allows the compiler to check for dimensional consistency.
Modelling of multivariate densities is a core component in many signal processing, pattern recognition and machine learning applications. The modelling is often done via Gaussian mixture models (GMMs), which use computationally expensive…
Parallelization is needed everywhere, from laptops and mobile phones to supercomputers. Among parallel programming models, task-based programming has demonstrated a powerful potential and is widely used in high-performance scientific…
In this paper we extend test set based augmentation methods for integer linear programs to programs with more general convex objective functions. We show existence and computability of finite test sets for these wider problem classes by…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…