Mathematical Software
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.
Large symmetric eigenvalue problems are commonly observed in many disciplines such as Chemistry and Physics, and several libraries including cuSOLVERMp, MAGMA and ELPA support computing large eigenvalue decomposition on multi-GPU or…
The DEViaN-LM is a R package that allows to detect the values poorly explained by a Gaussian linear model. The procedure is based on the maximum of the absolute value of the studentized residuals, which is a free statistic of the parameters…
From the beginning, the GraphBLAS were designed for ``nonblocking execution''; i.e., calls to GraphBLAS methods return as soon as the arguments to the methods are validated and define a directed acyclic graph (DAG) of GraphBLAS operations.…
Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…
MaRDI Open Interfaces is a software project aimed at improving reuse and interoperability in Scientific Computing by alleviating the difficulties of crossing boundaries between different programming languages, in which numerical packages…
Many multiphysics simulations involve processes evolving on disparate time scales, posing a challenge for efficient coupling. A naive approach that synchronizes all processes using the smallest time scale wastes computational resources on…
This paper presents evomap, a Python package for dynamic mapping. Mapping methods are widely used across disciplines to visualize relationships among objects as spatial representations, or maps. However, most existing statistical software…
Simultaneous variable selection and robust data fitting are important aspects of many mathematical modelling projects and a wide array of optimisation tools and techniques exist to support them. When the intention is to embed this…
The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their…
We present a straightforward and verified method of deciding whether the n-dimensional point x (n>=1), such that \nabla f(x)=0, is the local minimizer, maximizer or just a saddle point of a real-valued function f. The method scales linearly…
Many interesting phenomena are characterized by the complex interaction of different physical processes, each often best modeled numerically via a specific approach. In this paper, we present the design and implementation of an…
We extend the GenTen tensor decomposition package by introducing an accelerated dense matricized tensor times Khatri-Rao product (MTTKRP), the workhorse kernel for canonical polyadic (CP) tensor decompositions, that is portable and…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
Low-discrepancy (LD) sequences have been extensively used as efficient experimental designs across many scientific disciplines. QMCPy (https://qmcsoftware.github.io/QMCSoftware/) is an accessible Python library which provides a unified…
Sparse linear algebra is a cornerstone of many scientific computing and machine learning applications. Python has become a popular choice for these applications due to its simplicity and ease of use. Yet high performance sparse kernels in…
Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…
In this work, we investigate improving the runtime performance of key computational kernels in the Python Tensor Toolbox (pyttb), a package for analyzing tensor data across a wide variety of applications. Recent runtime performance…
We present a software implementation integrating the time-integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. This enables compact and scalable codes for multi-stage, multi-step, and adaptive…
The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had succesful applications in both mathematics and theoretical physics. This work deals with generalizations of the…