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Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel hardware due to synchronization bottlenecks.…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-01-29 Jeffrey Cornelis , Siegfried Cools , Wim Vanroose

The increasing complexity of deep learning recommendation models (DLRM) has led to a growing need for large-scale distributed systems that can efficiently train vast amounts of data. In DLRM, the sparse embedding table is a crucial…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-07 Xin Zhang , Quanyu Zhu , Liangbei Xu , Zain Huda , Wang Zhou , Jin Fang , Dennis van der Staay , Yuxi Hu , Jade Nie , Jiyan Yang , Chunzhi Yang

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…

Sparse matrices and linear algebra are at the heart of scientific simulations. More than 70 sparse matrix storage formats have been developed over the years, targeting a wide range of hardware architectures and matrix types. Each format is…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-15 Chris Stylianou , Michele Weiland

HPC systems are a critical resource for scientific research. The increased demand for computational power and memory ushers in the exascale era, in which supercomputers are designed to provide enormous computing power to meet these needs.…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-11 Yehonatan Fridman , Yaniv Snir , Harel Levin , Danny Hendler , Hagit Attiya , Gal Oren

The parallel simulation of Spiking Neural P systems is mainly based on a matrix representation, where the graph inherent to the neural model is encoded in an adjacency matrix. The simulation algorithm is based on a matrix-vector…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-09 Javier Hernández-Tello , Miguel Ángel Martínez-del-Amor , David Orellana-Martín , Francis George C. Cabarle

Modern compute nodes in high-performance computing provide a tremendous level of parallelism and processing power. However, as arithmetic performance has been observed to increase at a faster rate relative to memory and network bandwidths,…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-11 Johannes Pekkilä , Miikka S. Väisälä , Maarit J. Käpylä , Matthias Rheinhardt , Oskar Lappi

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation,…

Optimization and Control · Mathematics 2019-09-10 Jose S. Rodriguez , Carl D. Laird , Victor M. Zavala

This paper presents implementation details and empirical results for a hybrid message passing and shared memory paralleliziation of the adaptive integral method (AIM). AIM is implemented on a (near) petaflop supercomputing cluster of…

Computational Engineering, Finance, and Science · Computer Science 2010-10-08 Fangzhou Wei , Ali E. Yılmaz

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…

Numerical Analysis · Mathematics 2015-06-01 Mathias Jacquelin , Lin Lin , Chao Yang

Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting…

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring…

Numerical Analysis · Mathematics 2016-03-31 Tania Bakhos , Peter Kitanidis , Scott Ladenheim , Arvind K. Saibaba , Daniel Szyld

This paper presents the results of a preliminary experimental investigation of the performance of a stationary iterative method based on a block staircase splitting for solving singular systems of linear equations arising in Markov chain…

Numerical Analysis · Mathematics 2023-02-16 V. Besozzi , M. Della Bartola , L. Gemignani

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-18 Roman Iakymchuk , Maria Barreda , Stef Graillat , Jose I. Aliaga , Enrique S. Quintana-Orti

Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…

Machine Learning · Computer Science 2026-05-29 Kyuil Sim , Sanghyeok Choi , Jinkyoo Park

This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation…

Numerical Analysis · Mathematics 2025-01-14 Yingjie Zhou , Changqing Ye , Yucheng Liu , Shubin Fu , Eric T. Chung

It is shown in this paper that, almost all current prevalent iterative \mbox{methods} for solving linear system of equations can be classified as what we called extended Krylov subspace methods. In this paper a new type of iterative methods…

Numerical Analysis · Mathematics 2016-03-18 Wujian Peng , Shuhua Zhang

Scaling up hardware systems has become an important tactic for improving performance as Moore's law fades. Unfortunately, simulations of large hardware systems are often a design bottleneck due to slow throughput and long build times. In…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-31 Steven Herbst , Noah Moroze , Edgar Iglesias , Andreas Olofsson

This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…

Quantum Physics · Physics 2026-04-03 Tong Shen , Zeru Zhu , Ji Liu

Program implementation and simulation are essential for research in the field of quantum algorithms. However, complex and large-scale quantum algorithms can pose challenges for existing quantum programming languages and simulators. Here, we…

Quantum Physics · Physics 2023-03-14 Zhao-Yun Chen , Cheng Xue , Xi-Ning Zhuang , Tai-Ping Sun , Huan-Yu Liu , Ye Li , Yu-Chun Wu , Guo-Ping Guo