# Reading Course in Numerical Analysis

## What is it?

The reading course is a medium-term (typically one semester or so) group study of a specific topic, based on periodic sessions. The course sessions last two hours and are scheduled bi-weekly (see the calendar below for further details).

A paper or a chapter from a book is discussed during each meeting and presented by one of the attendees. The topics are chosen among relevant trends in Numerical Analysis and Linear Algebra and are based on requests from the audience.

Anybody is welcome to join, and Ph.D. and master’s students are particularly encouraged to participate.

The reading course takes place at the Department of Mathematics. It is currently coordinated by Fabio Durastante, Stefano Massei, and Leonardo Robol (if you wish to join the group just let us know!).

Just subscribe to the reading course mailing list. All communications will be delivered there.

## Calendar and Topics

### Fall 2022: Randomized Linear Algebra

This session is concerned with randomized methods for linear systems, eigenvalue problems, least squares, factorizations, low-rank approximation, and trace estimation problems.

• 03/10/2022, 14:00–16:00, Aula Riunioni
Introduction to randomized low-rank approximation: randomized embeddings [1, Chapters 6-10].
Speaker: Angelo Casulli.
• 17/10/2022, 14:00–16:00, Aula Riunioni
Randomized range finder, interpolative decompositions, and Randomized SVD [1, Chapters 11-14] and [2].
Speaker: Alberto Bucci.
• 07/11/2022, 14:00–16:00, Aula Riunioni
Randomized least squares: Blendenpik [3].
Speaker: Chiara Faccio.
• 21/11/2022, 14:00–16:00, Aula Riunioni
Randomized methods for eigenvalues and linear systems [4].
Speaker: Igor Simunec.
• 05/12/2022, 14:00–16:00, Aula Riunioni
Hutch++: Optimal stochastic trace estimation [5].
Speaker: Michele Rinelli.
• 19/12/2022, 14:00–16:00, Aula Riunioni
TBD

### Bibliography

[1] Randomized numerical linear algebra: Foundations and algorithms, Martinsson and Tropp, Acta Numerica, 2020.
[2] Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, Haiko et. al, SIAM review, 2011.
[3] Blendenpik: Supercharging LAPACK’S least-squares solver, Avron et. al, SISC, 2010.
[4] Fast & accurate randomized algorithms for linear systems and eigenvalue problems, Nakatsukasa and Tropp, arXiv, 2021.
[5] Hutch++: Optimal stochastic trace estimation, Meyer et. al, SIAM, 2021.
[6] Norm and trace estimation with random rank one vectors, Bujanovic and Kressner, SIMAX, 2021.
[7] Input sparsity time low-rank approximation via Ridge leverage score sampling, Cohen et. al, SIAM, 2017.
[8] Random matrix theory, Edelman and Rao, Acta Numerica, 2005.