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Lutz F. Gruber, Mike West
We discuss modeling and GPU-based computation in a new class of multivariate dynamic models customized to learning and prediction with increasingly high-dimensional time series. This defines an approach to decoupling analysis into a parallel set of univariate time series dynamic models, while flexibly modeling cross-series relationships in a novel, induced class of time-varying graphical models […]
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Vladica Andrejic, Milos Tatarevic
Kurepa’s conjecture states that there is no odd prime p which divides !p=0!+1!+…+(p-1)!. We search for a counterexample of this conjecture for all p<10^10. We introduce new optimization techniques and perform the computation using graphics processing units (GPUs). Additionally, we consider the generalized Kurepa’s left factorial given as !kn=(0!)k+(1!)k+…+((n-1)!)k and show that for all integers […]
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Sergiy Gogolenko, Zhaojun Bai, Richard Scalettar
We present a block structured orthogonal factorization (BSOF) algorithm and its parallelization for computing the inversion of block p-cyclic matrices.We aim at the high performance on multicores with GPU accelerators. We provide a quantitative performance model for optimal host-device load balance, and validate the model through numerical tests. Benchmarking results show that the parallel BSOF […]
Alexander Efremov, Eugenya Karepova, Vladimir Shaydurov, Alexander Vyatkin
A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture com-putation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation […]
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Volodymyr Kindratenko
This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and […]
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Sardar Anisul Haquen, Xin Li, Farnam Mansouri, Marc Moreno Maza, Wei Pan, Ning Xie
CUMODP is a CUDA library for exact computations with dense polynomials over finite fields. A variety of operations like multiplication, division, computation of subresultants, multi-point evaluation, interpolation and many others are provided. These routines are primarily designed to offer GPU support to polynomial system solvers and a bivariate system solver is part of the library. […]
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Orti, Alfredo Remon
The solution of large-scale Lyapunov equations is an important tool for the solution of several engineering problems arising in optimal control and model order reduction. In this work we investigate the case when the coefficient matrix of the equations presents a band structure. Exploiting the structure of this matrix we can achive relevant reductions in […]
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Yan Zhou
The sequential Monte Carlo (smc) methods have been widely used for modern scientific computation. Bayesian model comparison has been successfully applied in many fields. Yet there have been few researches on the use of smc for the purpose of Bayesian model comparison. This thesis studies different smc strategies for Bayesian model computation. In addition, various […]
Tor Gillberg, Are Magnus Bruaset, Oyvind Hjelle, Mohammed Sourouri
Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. […]
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Hasse Lovgren
CONTEXT: Reinforcement Learning (RL) is a time consuming effort that requires a lot of computational power as well. There are mainly two approaches to improving RL efficiency, the theoretical mathematics and algorithmic approach or the practical implementation approach. In this study, the approaches are combined in an attempt to reduce time consumption. OBJECTIVES: We investigate […]
Anastasia Kruchinina
Parallel computing is a topic that became very popular in the last few decades. Parallel computers are being used in many different areas of science such as astrophysics, climate modelling, quantum chemistry, fluid dynamics and medicine. Parallel programming is a type of programming where computations can be performed concurrently on different processors or devices. There […]
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Matthias Bartelt, Michael Gross
This paper deals with a Galerkin-based multi-scale time integration of a viscoelastic rope model. Using Hamilton’s dynamical formulation, Newton’s equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined […]
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