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Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In high performance computing environments, we observe an ongoing increase in the available numbers of cores. This development calls for re-emphasizing performance (scalability) analysis and speedup laws as suggested in the literature…
Parallel algorithms for ab initio calculations of vibrations modes of solids are presented and implemented under PVM. Load balancing and communication problems are dealt with in order to increase parallelism efficiency. For accurate time…
Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. In contrast to many algorithmic procedures, GP models are based on a statistical framework, which…
Approximate Bayesian Computation (ABC) is a widely applicable and popular approach to estimating unknown parameters of mechanistic models. As ABC analyses are computationally expensive, parallelization on high-performance infrastructure is…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
This paper proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for…
The standard kinetic Monte Carlo algorithm is an extremely efficient method to carry out serial simulations of dynamical processes such as thin-film growth. However, in some cases it is necessary to study systems over extended time and…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees,…
Neural algorithmic reasoners are parallel processors. Teaching them sequential algorithms contradicts this nature, rendering a significant share of their computations redundant. Parallel algorithms however may exploit their full…
Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought…
This paper is focused on evaluating the effect of some different techniques in machine learning speed-up, including vector caches, parallel execution, and so on. The following content will include some review of the previous approaches and…
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
We initiate the study of approximate maximum matching in the vertex partition model, for graphs subject to dynamic changes. We assume that the $n$ vertices of the graph are partitioned among $k$ players, who execute a distributed algorithm…
In this paper we study the limitations of parallelization in convex optimization. A convenient approach to study parallelization is through the prism of \emph{adaptivity} which is an information theoretic measure of the parallel runtime of…
The recent Natural Language Processing techniques have been refreshing the state-of-the-art performance at an incredible speed. Training huge language models is therefore an imperative demand in both industry and academy. However, huge…
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…
In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we…