Tue, 26 Oct 2021

14:00 - 14:30
L3

Randomized algorithms for trace estimation

Alice Cortinovis
(EPFL)
Abstract

The Hutchinson’s trace estimator approximates the trace of a large-scale matrix A by computing the average of some quadratic forms involving A and some random vectors. Hutch++ is a more efficient trace estimation algorithm that combines this with the randomized singular value decomposition, which obtains a low-rank approximation of A by multiplying the matrix with some random vectors. In this talk, we present an improved version of Hutch++ which aims at minimizing the computational cost - that is, the number of matrix-vector multiplications with A - needed to achieve a trace estimate with a target accuracy. This is joint work with David Persson and Daniel Kressner.

Watch our student lectures

As the new academic year approaches, we're adding to our catalogue of Oxford Mathematics student lectures on our YouTube Channel.

The latest is a lecture from Vicky Neale (pictured) on Monotonic Sequences, part of her first year Analysis 1 course. There are 50 more lectures for you to watch on the Channel covering many aspects of the undergraduate degree, including two full courses. We will add more over the coming weeks, including more lectures from the third and fourth years when students get to specialise.

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Symplectic duality - a research case study from Andrew Dancer

One of the main themes of geometry in recent years has been the appearance of unexpected dualities between different geometric spaces arising from ideas in mathematical physics. One famous such example is mirror symmetry. Another kind of duality, which I am currently investigating with collaborators from Oxford and Imperial College, is symplectic duality.

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