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"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: https://truetheta.io/concepts/linear-...
SOCIAL MEDIA
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SUPPORT
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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
Watch video Is the Future of Linear Algebra.. Random? online without registration, duration hours minute second in high quality. This video was added by user Mutual Information 08 April 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 389,079 once and liked it 14 thousand people.