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Related papers: Compressed Basis GMRES on High Performance GPUs

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Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-03-21 Bogdan Oancea , Richard Pospisil

A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern graphics processing units (GPUs). This format extends the standard compressed row storage (CRS) format and can be…

Computational Physics · Physics 2014-04-29 Zbigniew Koza , Maciej Matyka , Sebastian Szkoda , Łukasz Mirosław

In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these…

Numerical Analysis · Mathematics 2025-11-19 Tom Werner , Ning Wan , Agnieszka Miedlar

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…

Numerical Analysis · Mathematics 2017-04-05 Lijian Jiang , Qiuqi Li

This paper deals with linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetic using double precision. An analysis of their uses within iterative Krylov methods is presented to solve acoustic problems.…

Numerical Analysis · Mathematics 2021-12-23 Abal-Kassim Cheik Ahamed , Frederic Magoules

Clustering is an important tool in data analysis, with K-means being popular for its simplicity and versatility. However, it cannot handle non-linearly separable clusters. Kernel K-means addresses this limitation but requires a large kernel…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-29 Julian Bellavita , Matthew Rubino , Nakul Iyer , Andrew Chang , Aditya Devarakonda , Flavio Vella , Giulia Guidi

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…

Mathematical Software · Computer Science 2015-09-15 Weifeng Liu , Brian Vinter

To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure…

The Nonlinear GMRES (NGMRES) proposed by Washio and Oosterlee [Electron. Trans. Numer. Anal, 6(271-290), 1997] is an acceleration method for fixed point iterations. It has been demonstrated to be effective, but its convergence properties…

Numerical Analysis · Mathematics 2026-02-11 Chen Greif , Yunhui He

Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…

Numerical Analysis · Mathematics 2023-07-11 Noaman Khan , Erin Carson

Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…

Numerical Analysis · Mathematics 2021-12-08 Pietro Benedusi , Gioele Janett , Luca Belluzzi , Rolf Krause

In this paper, we study the restarted Krylov subspace method, which is typically represented by the GMRES(m) method. Our work mainly focused on the amount of change in the iterative solution of GMRES(m) at each restart. We propose an…

Numerical Analysis · Mathematics 2018-10-25 Hou-biao Li , Peng-hui He , Shao-Liang Zhang

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-10-25 Antonio Wendell De Oliveira Rodrigues , Frédéric Guyomarch , Yvonnick Le Menach , Jean-Luc Dekeyser

This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI…

Mathematical Software · Computer Science 2017-01-24 Hui Liu , Zhangxin Chen

In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast…

Numerical Analysis · Mathematics 2021-03-23 M. El Guide , A. El Ichi , K. Jbilou

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the bottleneck kernel of sparse tensor decomposition. In this work, we propose a GPU-based algorithm design to address the key challenges in accelerating spMTTKRP computation,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-15 Sasindu Wijeratne , Rajgopal Kannan , Viktor Prasanna

The residual cutting (RC) method has been proposed for efficiently solving linear equations obtained from elliptic partial differential equations. Based on the RC, we have introduced the generalized residual cutting (GRC) method, which can…

Numerical Analysis · Computer Science 2018-02-02 Toshihiko Abe , Anthony Theodore Chronopoulos

As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…

Numerical Analysis · Mathematics 2025-09-12 Zijian Zhang , Rui Hong , Xuesong Chen , Shuting Cai

Sparse linear algebra kernels play a critical role in numerous applications, covering from exascale scientific simulation to large-scale data analytics. Offloading linear algebra kernels on one GPU will no longer be viable in these…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-19 Jieyang Chen , Chenhao Xie , Jesun S Firoz , Jiajia Li , Shuaiwen Leon Song , Kevin Barker , Mark Raugas , Ang Li

Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a…