What makes a good talk? This year, graduate students and postdocs will give a series talks on how to give talks! There may even be a small prize for the audience’s favourite.

If you’d like to have a go at informing, entertaining, or just have an axe to grind about a particularly bad talk you had to sit through, we’d love to hear from you (you can email Ric Wade or ask any of the organizers).
 

We consider the problem of approximating singular values of a matrix when provided with approximations to the leading singular vectors. In particular, we focus on the Generalized Nystrom (GN) method, a commonly used low-rank approximation, and its error in extracting singular values. Like other approaches, the GN approximation can be interpreted as a perturbation of the original matrix. Up to orthogonal transformations, this perturbation has a peculiar structure that we wish to exploit. Thus, we use the Jordan-Wieldant Theorem and similarity transformations to generalize a matrix perturbation theory result on eigenvalues of a perturbed Hermitian matrix. Finally, combining the above,  we can derive a bound on the GN singular values approximation error. We conclude by performing preliminary numerical examples. The aim is to heuristically study the sharpness of the bound, to give intuitions on how the analysis can be used to compare different approaches, and to provide ideas on how to make the bound computable in practice.