Related papers: pfd-parallel, a Singular/GPI-Space package for mas…
Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm under consideration modulo a number of primes and then lift…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
We present the parallel particle filtering (PPF) software library, which enables hybrid shared-memory/distributed-memory parallelization of particle filtering (PF) algorithms combining the Message Passing Interface (MPI) with multithreading…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
We present a computational framework for piecewise constant functions (PCFs) and use this for several types of computations that are useful in statistics, e.g., averages, similarity matrices, and so on. We give a linear-time,…
Compactly expressing large-scale datasets through Multivariate Functional Approximations (MFA) can be critically important for analysis and visualization to drive scientific discovery. Tackling such problems requires scalable data…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
We present FooPar, an extension for highly efficient Parallel Computing in the multi-paradigm programming language Scala. Scala offers concise and clean syntax and integrates functional programming features. Our framework FooPar combines…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…
We develop a novel parallel resampling algorithm for fully parallelized particle filters, which is designed with GPUs (graphics processing units) or similar parallel computing devices in mind. With our new algorithm, a full cycle of…
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Fortran's prominence in scientific computing requires strategies to ensure both that legacy codes are efficient on high-performance computing systems, and that the language remains attractive for the development of new high-performance…
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to…
Introducing parallelism and exploring its use is still a fundamental challenge for the computer algebra community. In high performance numerical simulation, on the other hand, transparent environments for distributed computing which follow…
Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…