*PCMI summer school lectures:*

**Randomized algorithms for matrix computations and analysis of high dimensional data**

*Lecturer: Per-Gunnar Martinsson (Univ. of Colorado at Boulder)*

*TA: Nathan Heavner (Univ. of Colorado at Boulder)*

This wepage is set up to provide convenient links to supplementary material for a series of three lectures and three problem solving sessions that formed a part of the PCMI program

The lectures will be self-contained, and will in principle assume only knowledge of basic material on linear algebra and probability theory. Some prior experience with numerical analysis would be helpful, but is far from necessary.

**Lecture slides.****Lecture summary.**This document provides a road map of the lectures. Some key concepts are described in detail. References are provided on where to look for further details.**Manuscript**. The material in the lectures is drawn largely from the manuscript linked to (arxiv.org report 1607.01649). This is the first half of a longer text currently in progress. Beware that the manuscript may very well contain errors of various types - if you see any then please contact the author! Other feedback is also very welcome. (Local copy.)**Survey paper.**While getting a few years old by now, this survey provides a detailed description of some of the techniques described. The survey is quite long, but the introduction (section 1.1 - 1.6) can be read by itself, and provides a concise introduction to the key ideas. I would also recommend an early PNAS paper that also provides a very brief treatment of the key concepts.**Problem sets.**Set 1, solutions, Set 2, solutions, Set 3.**Software:**- Tutorial codes implementing RSVD in Matlab. There is GPU support via Matlab (for supported machines).
- RSVDPACK (With Sergey Voronin.) CPU and GPU implementations in C of most of the techniques covered: RSVD, randomized ID and CUR, etc.
- ID (With Mark Tygert.) FORTRAN and Matlab codes for RSVD, RSFT, interpolative decompositions, etc.
- HGRRP (With Gregorio Quintana-Orti, Nathan Heavner, and Robert van de Geijn.) Highly optimized implementations of (Householder) column pivoted QR with randomization for pivoting. Functions with LAPACK compatible interfaces are included.

* Research support by:*