Article
Mathematics, Applied
Linjian Ma, Edgar Solomonik
Summary: This paper introduces a novel family of algorithms that use perturbative corrections to optimize the quadratic optimization subproblems in CP and Tucker decomposition. The proposed pairwise perturbation algorithms are easy to control and achieve convergenceto minima that are as good as ALS.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Hans De Sterck, Yunhui He
Summary: This study explores the application of nonlinear convergence acceleration methods in fixed-point iteration, confirming the significant improvement in asymptotic convergence behavior provided by methods such as Anderson acceleration and nonlinear GMRES. Theoretical quantification of this improvement is still lacking, motivating research under simplified conditions and numerical validation through coefficient optimization and comparison in the linear GMRES case.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Navjot Singh, Linjian Ma, Hongru Yang, Edgar Solomonik
Summary: The paper introduces a parallel implementation of the Gauss-Newton method for CP decomposition, which iteratively solves linear least squares problems to improve accuracy. It explores the convergence of the Gauss-Newton method compared to alternating least squares for finding exact and approximate CP decompositions.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Yajie Yu, Hanyu Li
Summary: In this paper, two strategies are proposed to tackle the high cost issue in tensor ring decomposition and three ALS-based algorithms are designed. By simplifying the calculation of coefficient matrices and stabilizing the ALS subproblems, the algorithms improve computational efficiency and numerical stability.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
David Evans, Nan Ye
Summary: This article proposes a new accelerated ALS algorithm that improves the convergence speed by using a blockwise strategy, momentum-based extrapolation technique, and random perturbation technique. The algorithm updates one factor matrix at a time, reducing reconstruction error, moving along previous update direction, and introducing random perturbation to break convergence bottlenecks. Empirical results show that the proposed algorithm outperforms state-of-the-art techniques on both simulated and real tensors.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2023)
Article
Operations Research & Management Science
Yuning Yang
Summary: This paper investigates the application of alternating least squares in tensor canonical polyadic approximation. It demonstrates alternative conditions for global convergence by weakening the positive definiteness assumption and discusses its connection to the uniqueness of exact CP decomposition.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Review
Engineering, Multidisciplinary
Maolin Liang, Lifang Dai
Summary: Recent research on the multilinear system Axm-1=b with tensor A of order-m and dimension-n and vector b of dimension-n has focused on its applications in data mining, numerical PDEs, tensor complementary problems, etc. This paper introduces an alternating minimization method for solving this system and presents randomized versions to enhance performance, with numerical experiments demonstrating their superiority over existing methods in the same scenarios.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Computer Science, Software Engineering
Christos Psarras, Lars Karlsson, Rasmus Bro, Paolo Bientinesi
Summary: This article introduces how to fuse multiple decompositions of the same tensor at the algorithmic level to increase arithmetic intensity, improve computation efficiency, and be compatible with common ALS enhancements. Experimental results demonstrate that this approach can reduce completion time.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2022)
Article
Automation & Control Systems
Kristian Hovde Liland, Ulf Geir Indahl, Joakim Skogholt, Puneet Mishra
Summary: The article discusses using multilinear partial least squares for analyzing multiway datasets, which allows for building parsimonious models handling various continuous and categorical responses. An advantage in computational speed is achieved by deflating responses and orthogonalising scores.
JOURNAL OF CHEMOMETRICS
(2022)
Article
Environmental Sciences
Hao Guo, Wenxing Bao, Wei Feng, Shasha Sun, Chunhui Mo, Kewen Qu
Summary: This paper proposes an improved hyperspectral image fusion algorithm that enhances the quality of fused images by eliminating scaling effects and counter-scaling effects through the introduction of different norms. The experimental results demonstrate that the proposed method outperforms existing methods in terms of visual results, metric evaluations, algorithm runtime, and classification results.
Article
Automation & Control Systems
Huiwen Yu, Dillen Augustijn, Rasmus Bro
Summary: This paper proposes novel extrapolation-based PARAFAC2 algorithms which achieve faster convergence speeds and outperform existing methods. A comprehensive investigation and comparison of various extrapolation algorithms is conducted using simulated and real data.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2021)
Article
Mathematics, Applied
Chuanfu Xiao, Chao Yang, Min Li
Summary: A new class of truncated HOSVD algorithms based on alternating least squares (ALS) is proposed in this paper for efficiently computing the low multilinear rank approximation of tensors. These ALS-based approaches eliminate the redundant computations of the singular vectors of intermediate matrices, thus avoiding data explosion issue and providing adjustable convergence tolerance, as well as intrinsic parallelizability on high-performance computers. Theoretical analysis shows that the ALS iteration in the proposed algorithms is q-linear convergent with wide convergence region, and numerical experiments demonstrate that ALS-based methods can substantially reduce the total cost of the original ones and are highly scalable for parallel computing.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Multidisciplinary
Suchuan Dong, Zongwei Li
Summary: The neural network-based method combines ELM, domain decomposition, and local neural networks to solve linear and nonlinear partial differential equations. It shows significant convergence with respect to neural network degrees of freedom and performs well in numerical experiments.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Operations Research & Management Science
Junwei Zhang, Yuning Yang
Summary: This paper examines modified versions of ALS and RALS algorithms for tensor decomposition. Two hybrid alternating methods, which combine the extra-gradient method with Newton's method, are proposed. The global convergence of the algorithm is analyzed under certain assumptions, and preliminary numerical experiments demonstrate the effectiveness of the proposed methods compared to standard ALS and RALS algorithms.
PACIFIC JOURNAL OF OPTIMIZATION
(2022)
Article
Engineering, Electrical & Electronic
Guoyong Zhang, Jun Wang, Qihang Peng, Xiaonan Chen, Shaoqian Li
Summary: The study proposes two novel radio map reconstruction algorithms based on tensor canonical polyadic decomposition to address the challenge of estimating dynamic radio maps in spectrum cartography. The DW-CPD and I-CPD algorithms show similar estimation performance for dynamic spectrum cartography and outperform existing methods, with I-CPD being more suitable for real-time applications due to its overall advantage in performance, running time, and storage.
Article
Public, Environmental & Occupational Health
John C. Lang, Daniel M. Abrams, Hans De Sterck
Article
Mathematics, Applied
Hans de Sterck, Alexander Howse
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2016)
Article
Computer Science, Artificial Intelligence
Nayyar A. Zaidi, Geoffrey I. Webb, Mark J. Carman, Francois Petitjean, Wray Buntine, Mike Hynes, Hans De Sterck
Article
Multidisciplinary Sciences
John C. Lang, Hans De Sterck, Daniel M. Abrams
Article
Mathematics, Applied
Hans De Sterck, Alexander J. M. Howse
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2018)
Article
Biochemistry & Molecular Biology
Cyril F. Reboul, Simon Kiesewetter, Michael Eager, Matthew Belousoff, Tiangang Cui, Hans De Sterck, Dominika Elmlund, Hans Elmlund
JOURNAL OF STRUCTURAL BIOLOGY
(2018)
Article
Mathematics, Applied
Ulrich Ruede, Karen Willcox, Lois Curfman McInnes, Hans De Sterck
Article
Mathematics, Applied
L. Freret, L. Ivan, H. De Sterck, C. P. T. Groth
JOURNAL OF SCIENTIFIC COMPUTING
(2019)
Article
Mathematics, Applied
Alexander J. Howse, Hans De Sterck, Robert D. Falgout, Scott Maclachlan, Jacob Schroder
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
Article
Mathematics, Applied
Drew Mitchell, Nan Ye, Hans De Sterck
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2020)
Article
Mathematics, Applied
Hans De Sterck, Robert D. Falgout, Stephanie Friedhoff, Oliver A. Krzysik, Scott P. MacLachlan
Summary: This study applies parallel-in-time methods to the linear advection equation, improving coarse-grid operators through optimization techniques to achieve scalable convergence in just a handful of iterations.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Dawei Wang, Yunhui He, Hans De Sterck
Summary: Empirical results demonstrate that Anderson acceleration can enhance the asymptotic linear convergence speed of the Alternating Direction Method of Multipliers (ADMM) when ADMM converges linearly. The paper explains and quantifies this improvement for a special case of a stationary version of Anderson acceleration applied to ADMM. Numerical results suggest that the optimal linear convergence factor of stationary AA method can give a useful estimate for the asymptotic linear convergence speed of the non-stationary AA method used in practice.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
H. De Sterck, R. D. Falgout, O. A. Krzysik, J. B. Schroder
Summary: Parallel-in-time methods for PDEs have been extensively studied and developed, but they perform poorly for advection-dominated problems. In this paper, we analyze the MGRIT algorithm for constant-wave-speed linear advection problems and propose an alternative coarse-grid operator that better corrects smooth Fourier modes. The proposed operator yields fast MGRIT convergence for various discretization methods and achieves speed-up over sequential time-stepping according to parallel results.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Interdisciplinary Applications
J. C. Lang, H. De Sterck
JOURNAL OF COMPLEX NETWORKS
(2016)
Article
Mathematics, Interdisciplinary Applications
John C. Lang, Hans De Sterck, Jamieson L. Kaiser, Joel C. Miller
JOURNAL OF COMPLEX NETWORKS
(2018)