RandNLA swMATH ID: 41749 Software Authors: Drineas, P.; Mahoney, M. W. Description: RandNLA: Randomized Numerical Linear Algebra. Matrices are ubiquitous in computer science, statistics, and applied mathematics. An m × n matrix can encode information about m objects (each described by n features), or the behavior of a discretized differential operator on a finite element mesh; an n × n positive-definite matrix can encode the correlations between all pairs of n objects, or the edge-connectivity between all pairs of nodes in a social network; and so on. Motivated largely by technological developments that generate extremely large scientific and Internet datasets, recent years have witnessed exciting developments in the theory and practice of matrix algorithms. Particularly remarkable is the use of randomizationtypically assumed to be a property of the input data due to, for example, noise in the data generation mechanismsas an algorithmic or computational resource for the development of improved algorithms for fundamental matrix problems such as matrix multiplication, least-squares (LS) approximation, low-rank matrix approximation, and Laplacian-based linear equation solvers. Homepage: https://www.stat.berkeley.edu/~mmahoney/pubs/RandNLA_in_CACM_2016.pdf Related Software: Tensorlab; rsvd; TensorToolbox; ARPACK; RSVDPACK; TensorToolbox.jl; UTV; randUTV; MNIST; Algorithm 862; cross2D; BCLS; redbKIT; Algorithm 971; BSDS; tproduct; GitHub; CVXPY; Gurobi; OSUMC Cited in: 25 Documents all top 5 Cited by 52 Authors 4 Che, Maolin 4 Wei, Yimin 3 Drineas, Petros 3 Kutz, J. Nathan 3 Yan, Hong 2 Brunton, Steven L. 2 Erichson, N. Benjamin 2 Ipsen, Ilse C. F. 2 Saibaba, Arvind Krishna 1 Alla, Alessandro 1 Aravkin, Aleksandr Y. 1 Buhr, Andreas 1 Casey, Michael P. 1 Chen, Ting-Li 1 Chowdhury, Agniva 1 de Sturler, Eric 1 Fuji, Terunari 1 Gu, Yu 1 Helmstetter, Anthony W. 1 Horesh, Lior 1 Huang, Suyun 1 Jian, Yuan 1 Kalantzis, Vassilis 1 Kilmer, Misha Elena 1 Kontopoulou, Eugenia-Maria 1 Li, Min 1 Li, Yaohang 1 Ma, Anna 1 Magdon-Ismail, Malik 1 Mahoney, Michael W. 1 Manohar, Krithika 1 Mathelin, Lionel 1 Minster, Rachel 1 Molitor, Denali 1 Ning, Yang 1 Paulino, Glaucio H. 1 Poirion, Pierre-Louis 1 Renaut, Rosemary Anne 1 Roosta, Fred 1 Ruppert, David 1 Smetana, Kathrin 1 Takeda, Akiko 1 Vatankhah, Saeed 1 Wang, Weichung 1 Xi, Yuanzhe 1 Xiao, Chuanfu 1 Yang, Chao 1 Yang, Jiasen 1 Yu, Wenjian 1 Zhang, Tao 1 Zhang, Xiaojia Shelly 1 Zheng, Peng all top 5 Cited in 16 Serials 5 SIAM Journal on Matrix Analysis and Applications 3 Journal of Scientific Computing 3 SIAM Journal on Scientific Computing 2 BIT 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational and Applied Mathematics 1 Statistics & Probability Letters 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Advances in Computational Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 Electronic Journal of Statistics 1 Journal of Computational and Graphical Statistics 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 9 Fields 19 Numerical analysis (65-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 8 Computer science (68-XX) 3 Statistics (62-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Functional analysis (46-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year