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Special Issue: Recent Advances in Fast Matrix and Tensor Computations

Guest Editors

Prof. Xian-Ming Gu
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
Email: guxm@swufe.edu.cn


Prof. Junfeng Yin
Department of Mathematics, Tongji University, Shanghai 200092, China
Email: yinjf@tongji.edu.cn


Prof. Bruno Carpentieri
Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Email: Bruno.Carpentieri@unibz.it


Dr. Yong-Liang Zhao
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China
Email: ylzhao@sicnu.edu.cn

Manuscript Topics

Matrix and tensor computations are at the core of a multitude of applications in diverse domains of scientific computing and data science. These computations present several challenges due to their complexity, high computational cost, and large memory footprint. While there is a widespread availability and use of general-purpose high-performance libraries for matrix computations on multicore CPUs and GPUs, the same is not true for tensor computations. Now, it seems that scientific advances on tensor and matrix computations are scattered and, despite there is a growing community working on tensor and matrix computations, researchers in this field have a rather limited visibility and tend to work in a compartmentalized fashion.


This Special Issue aims at bringing together many experts from distinct domains such as numerical solutions of PDEs, fractional differential equations and integro-differential equations, Image Processing and related topics, Computational electromagnetics, just to name a few, to uncover computational challenges, bottlenecks, and advances in high-performance tensor and matrix computations arising in those disciplines. The aim is to enhance understanding of the similarities and differences in the tensor operations and computational tasks across these fields, and to seek pathways to general purpose software libraries and frameworks for high-performance tensor computations. This also takes into account the analytical and algebraic foundations of structured tensor and matrix decompositions and approximations. In the long term, the vision is to create a framework for tensor and matrix computations that is understandable by the many practitioners and can be utilized to carry out efficient, parallel, and high-performance tensor and matrix calculations.


We are interested in topics including but not limited to the following:
• Fractional integro-differential equations (of any type) and their generalisations
• Methodologies for solving (variable-order) fractional differential equations
• Applications of fractional calculus to real-world problems
• Parallel-in-time algorithms and applications
• Numerical linear algebra with applications
• Computational electromagnetics
• The model of image processing and its efficient methods
• Tensor analysis and computations
• Low-rank matrix and tensor approximations
• Randomized matrix algorithms


Keywords  
Fractional differential equations, partial differential equations, numerical and approximation methods, parallel-in-time methods, applications of fractional calculus, numerical linear algebra, matrix and tensor computations, image processing, Computational electromagnetics.


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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 30 June 2022

Published Papers(20)

Theory article
A numerical method for parabolic complementarity problem
Haiyan Song Fei Sun
2023, Volume 31, Issue 2: 1048-1064. doi: 10.3934/era.2023052
Abstract HTML PDF Viewed (1894)
Research article
A hybrid algorithm based on parareal and Schwarz waveform relaxation
Liping Yang Hu Li
2022, Volume 30, Issue 11: 4086-4107. doi: 10.3934/era.2022207
Abstract HTML PDF Viewed (1912)
Research article
A high-order numerical scheme for right Caputo fractional differential equations with uniform accuracy
Li Tian Ziqiang Wang Junying Cao
2022, Volume 30, Issue 10: 3825-3854. doi: 10.3934/era.2022195
Abstract HTML PDF Cited (1) Viewed (2441)
Research article
Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation
Mingfa Fei Wenhao Li Yulian Yi
2022, Volume 30, Issue 10: 3635-3659. doi: 10.3934/era.2022186
Abstract HTML PDF Cited (4) Viewed (2223)
Research article
New error bounds for the tensor complementarity problem
Xin Liu Guang-Xin Huang
2022, Volume 30, Issue 6: 2196-2204. doi: 10.3934/era.2022111
Abstract HTML PDF Cited (5) Viewed (1738)
Research article
Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
Natália Bebiano João da Providência Wei-Ru Xu
2022, Volume 30, Issue 5: 1864-1880. doi: 10.3934/era.2022094
Abstract HTML PDF Viewed (2237)
Research article
High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format
Lot-Kei Chou Siu-Long Lei
2022, Volume 30, Issue 4: 1463-1476. doi: 10.3934/era.2022077
Abstract HTML PDF Viewed (2319)
Research article
The parameter-Newton iteration for the second-order cone linear complementarity problem
Peng Zhou Teng Wang
2022, Volume 30, Issue 4: 1454-1462. doi: 10.3934/era.2022076
Abstract HTML PDF Viewed (2017)
Research article
Localization and calculation for C-eigenvalues of a piezoelectric-type tensor
Shunjie Bai Caili Sang Jianxing Zhao
2022, Volume 30, Issue 4: 1419-1441. doi: 10.3934/era.2022074
Abstract HTML PDF Viewed (2492)
Research article
On global randomized block Kaczmarz method for image reconstruction
Ranran Li Hao Liu
2022, Volume 30, Issue 4: 1442-1453. doi: 10.3934/era.2022075
Abstract HTML PDF Cited (4) Viewed (2732)
Research article
Numerical analysis of variable-order fractional KdV-Burgers-Kuramoto equation
Leilei Wei Xiaojing Wei Bo Tang
2022, Volume 30, Issue 4: 1263-1281. doi: 10.3934/era.2022066
Abstract HTML PDF Cited (4) Viewed (2813)
Research article
Greedy randomized and maximal weighted residual Kaczmarz methods with oblique projection
Fang Wang Weiguo Li Wendi Bao Li Liu
2022, Volume 30, Issue 4: 1158-1186. doi: 10.3934/era.2022062
Abstract HTML PDF Cited (2) Viewed (2786)
Research article
A generalization of the AOR iteration method for solving absolute value equations
Cui-Xia Li
2022, Volume 30, Issue 3: 1062-1074. doi: 10.3934/era.2022056
Abstract HTML PDF Cited (5) Viewed (2293)
Research article
SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations
Chunye Gong Mianfu She Wanqiu Yuan Dan Zhao
2022, Volume 30, Issue 3: 943-960. doi: 10.3934/era.2022049
Abstract HTML PDF Viewed (2344)
Research article
A class of fourth-order Padé schemes for fractional exotic options pricing model
Ming-Kai Wang Cheng Wang Jun-Feng Yin
2022, Volume 30, Issue 3: 874-897. doi: 10.3934/era.2022046
Abstract HTML PDF Cited (3) Viewed (2410)
Research article
Block splitting preconditioner for time-space fractional diffusion equations
Jia-Min Luo Hou-Biao Li Wei-Bo Wei
2022, Volume 30, Issue 3: 780-797. doi: 10.3934/era.2022041
Abstract HTML PDF Viewed (2221)
Research article
A two-step randomized Gauss-Seidel method for solving large-scale linear least squares problems
Yimou Liao Tianxiu Lu Feng Yin
2022, Volume 30, Issue 2: 755-779. doi: 10.3934/era.2022040
Abstract HTML PDF Cited (5) Viewed (2791)
Research article
Acceleration of the generalized FOM algorithm for computing PageRank
Yu Jin Chun Wen Zhao-Li Shen
2022, Volume 30, Issue 2: 732-754. doi: 10.3934/era.2022039
Abstract HTML PDF Viewed (2206)
Research article
A structure-preserving doubling algorithm for solving a class of quadratic matrix equation with $ M $-matrix
Cairong Chen
2022, Volume 30, Issue 2: 574-584. doi: 10.3934/era.2022030
Abstract HTML PDF Cited (2) Viewed (2243)
Research article
Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model
Yining Yang Yang Liu Cao Wen Hong Li Jinfeng Wang
2022, Volume 30, Issue 2: 440-458. doi: 10.3934/era.2022023
Abstract HTML PDF Cited (1) Viewed (2358)