Mathematical Software
Recent trends and advancement in including more diverse and heterogeneous hardware in High-Performance Computing is challenging software developers in their pursuit for good performance and numerical stability. The well-known maxim…
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gau{\ss}-Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with…
We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with…
Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to…
NetworkDynamics.jl is an easy-to-use and computationally efficient package for working with heterogeneous dynamical systems on complex networks, written in Julia, a high-level, high-performance, dynamic programming language. By combining…
SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. In the last years we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These…
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation…
MLPACK is a state-of-the-art, scalable, multi-platform C++ machine learning library released in late 2011 offering both a simple, consistent API accessible to novice users and high performance and flexibility to expert users by leveraging…
Updating a linear least squares solution can be critical for near real-time signalprocessing applications. The Greville algorithm proposes a simple formula for updating the pseudoinverse of a matrix A $\in$ R nxm with rank r. In this paper,…
This paper presents a systematic review of Python packages with a focus on time series analysis. The objective is to provide (1) an overview of the different time series analysis tasks and preprocessing methods implemented, and (2) an…
Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open source C++ software toolbox for…
Bayesian Knowledge Tracing, a model used for cognitive mastery estimation, has been a hallmark of adaptive learning research and an integral component of deployed intelligent tutoring systems (ITS). In this paper, we provide a brief history…
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
The R package micompr implements a procedure for assessing if two or more multivariate samples are drawn from the same distribution. The procedure uses principal component analysis to convert multivariate observations into a set of linearly…
Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtained is often not available. Especially in the scientific…
We present the main improvements and new features in version $\texttt{2.0}$ of the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid…
Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…
We present the VECMA toolkit (VECMAtk), a flexible software environment for single and multiscale simulations that introduces directly applicable and reusable procedures for verification, validation (V&V), sensitivity analysis (SA) and…
Transformer, BERT and their variants have achieved great success in natural language processing. Since Transformer models are huge in size, serving these models is a challenge for real industrial applications. In this paper, we propose…
The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis…