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Title:Is the Future of Linear Algebra.. Random?

The machine learning consultancy: Join my email list to get educational and useful articles (and nothing else!): Want to work together? See here: "Randomization is arguably the most exciting and innovative idea to have hit linear algebra in a long time." - First line of the Blendenpik paper, H. Avron et al. Follow up post: SOCIAL MEDIA LinkedIn : Twitter : Github: SUPPORT SOURCES Source [1] is the paper that caused me to create this video. [3], [7] and [8] provided a broad and technical view of randomization as a strategy for NLA. [9] and [12] informed me about the history of NLA. [2], [4], [5], [6], [10], [11], [13] and [14] provide concrete algorithms demonstrating the utility of randomization. [1] Murray et al. Randomized Numerical Linear Algebra. arXiv:2302.11474v2 2023 [2] Melnichenko et al. CholeskyQR with Randomization and Pivoting for Tall Matrices (CQRRPT). arXiv:2311.08316v1 2023 [3] P. Drineas and M. Mahoney. RandNLA: Randomized Numerical Linear Algebra. Communications of the ACM. 2016 [4] N. Halko, P. Martinsson, and J. Tropp. Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions. arXiv:0909.4061v2 2010 [5] Tropp et al. Fixed Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data. NeurIPS Proceedings. 2017 [6] X. Meng, M. Saunders, and M. Mahoney. LSRN: A Parallel Iterative Solver for Strongly Over- Or Underdetermined Systems. SIAM 2014 [7] D. Woodruff. Sketching as a Tool for Numerical Linear Algebra. IBM Research Almaden. 2015 [8] M. Mahoney. Randomized Algorithms for Matrices and Data. arXiv:1104.5557v3. 2011 [9] G. Golub and H van der Vorst. Eigenvalue Computation in the 20th Century. Journal of Computational and Applied Mathematics. 2000 [10] J. Duersch and M. Gu. Randomized QR with Column Pivoting. arXiv:1509.06820v2 2017 [11] Erichson et al. Randomized Matrix Decompositions Using R. Journal of Statistical Software. 2019 [12] J. Gentle et al. Software for Numerical Linear Algebra. Springer. 2017 [13] H. Avron, P. Maymounkov, and S. Toledo. Blendenpik: Supercharging LAPACK's Least-Squares Solver. Siam. 2010 [14] M. Mahoney and P. Drineas. CUR Matrix Decompositions for Improved Data Analysis. Proceedings of the National Academy of Sciences. 2009 TIMESTAMPS 0:00 Significance of Numerical Linear Algebra (NLA) 1:35 The Paper 2:20 What is Linear Algebra? 5:57 What is Numerical Linear Algebra? 8:53 Some History 12:22 A Quick Tour of the Current Software Landscape 13:42 NLA Efficiency 16:06 Rand NLA's Efficiency 18:38 What is NLA doing (generally)? 20:11 Rand NLA Performance 26:24 What is NLA doing (a little less generally)? 31:30 A New Software Pillar 32:43 Why is Rand NLA Exceptional? 34:01 Follow Up Post and Thank You's


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