Randomized matrix computations: themes and variations

Creators: Kireeva, Anastasia; Tropp, Joel A.¹

1. California Institute of Technology

Abstract

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is illustrated by its application to several computational problems. This treatment establishes conceptual foundations for randomized numerical linear algebra, and it forges links between algorithms that may initially seem unrelated.

Copyright and License

Acknowledgement

JAT is grateful to Massimo Fornasier and the other organizers of the 2023 CIME Summer School on Machine Learning for the invitation to give these lectures and to spend a week in Cetraro, Calabria. (“Vi ravviso, o luoghi ameni!”) JAT recognizes generous grant support from ONR Award N00014-18-1-2363, NSF FRG Award 1952777, and the Caltech Carver Mead New Adventures Fund that made possible the research, writing, and travel. Additional financial and administrative support were provided by CIME and by the Mathematics Department of TU-Munich.

AK expresses gratitude to the organizers of the 2023 CIME Summer School on Machine Learning and CIME for their support, which made her participation in the school and writing these notes possible.

We would like to thank Ethan Epperly for a close reading and suggestions for improvements.

Additional Information

Lectures: Cetraro, July 3–7, 2023. Notes: February 20, 2024. Revised: April 2, 2024.

2020 Mathematics Subject Classification. 15-02; 60-02; 65-02

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