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The partial Latin square extension problem is to fill as many as possible empty cells of a partially filled Latin square. This problem is a useful model for a wide range of applications in diverse domains. This paper presents the first…

Artificial Intelligence · Computer Science 2022-02-11 Olivier Goudet , Jin-Kao Hao

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Numerical Analysis · Mathematics 2022-02-25 Qichen Hong , Hehu Xie , Fei Xu

In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…

Numerical Analysis · Mathematics 2011-07-04 Qun Lin , Hehu Xie

Over the past 30 years many researchers in the field of evolutionary computation have put a lot of effort to introduce various approaches for solving hard problems. Most of these problems have been inspired by major industries so that…

Neural and Evolutionary Computing · Computer Science 2016-06-23 Mohammad Reza Bonyadi , Zbigniew Michalewicz , Frank Neumann , Markus Wagner

A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…

Numerical Analysis · Mathematics 2019-08-30 A. A. Alikhanov , A. M. Apekov , Z. A. Kokov , A. O. Belyaev , L. A. Khamukova

We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…

Statistics Theory · Mathematics 2020-12-04 Samprit Banerjee , Stefano Monni

It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…

Numerical Analysis · Mathematics 2025-09-24 Xiaoying Dai , Yan Li , Bin Yang , Aihui Zhou

Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…

Numerical Analysis · Mathematics 2017-04-19 Victor Y. Pan

The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for…

Artificial Intelligence · Computer Science 2025-01-03 Zongbiao Li , Xiezhao Li , Yinghao Cui , Yijun Chen , Zhixuan Gu , Yuxuan Liu , Wenbo Zhu , Fei Jia , Ke Liu , Qifeng Li , Junyao Zhan , Jiangtao Zhou , Chenxi Zhang , Qike Liu

Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…

Neural and Evolutionary Computing · Computer Science 2015-08-04 Ka-Chun Wong

An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…

Computational Physics · Physics 2009-11-10 W. R. Gibbs

In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…

Numerical Analysis · Mathematics 2015-06-23 Hehu Xie

Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-19 Edgar Solomonik , Grey Ballard , James Demmel , Torsten Hoefler

We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…

Numerical Analysis · Mathematics 2010-02-05 Noureddine El Karoui , Alexandre d'Aspremont

Evolutionary algorithms (EAs) are increasingly implemented on graphics processing units (GPUs) to leverage parallel processing capabilities for enhanced efficiency. However, existing studies largely emphasize the raw speedup obtained by…

Neural and Evolutionary Computing · Computer Science 2026-01-28 Xinmeng Yu , Tao Jiang , Ran Cheng , Yaochu Jin , Kay Chen Tan

We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…

Symbolic Computation · Computer Science 2014-02-17 Jean-Guillaume Dumas , Thierry Gautier , Clément Pernet , Ziad Sultan

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…

Data Structures and Algorithms · Computer Science 2011-11-16 Michael W. Mahoney

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding…

Numerical Analysis · Mathematics 2023-05-23 Yifan Wang , Hehi Xie

The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…

Numerical Analysis · Mathematics 2020-03-02 Ning Zhang , Xiaole Han , Yunhui He , Hehu Xie , Chun'guang You

Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the years. Recent advancements in evolutionary search with large…

Artificial Intelligence · Computer Science 2026-05-26 Anja Surina , Amin Mansouri , Lars Quaedvlieg , Amal Seddas , Maryna Viazovska , Emmanuel Abbe , Caglar Gulcehre