Datum predavanja: petak, 20.3.2026.
Vrijeme predavanja: 10h u B04

Luka Marohnić, Tehničko veleučilište u Zagrebu
Title: Randomised algorithms for computing resonances and quasi-resonances

Abstract:
We address the problem of locating quasi-resonances for a two-dimensional Helmholtz transmission problem on a prescribed frequency interval. Quasi-resonances are the local minima of the scalar function f, where f(k) equals the minimal singular value of the Calderón operator at frequency k. The map f is a lower envelope of a collection of finitely many analytic functions and may develop non-differentiable extrema due to singular-value crossings. Our solution proceeds in three stages:
(i) compute the minimal singular value using a randomized SVD accelerated by iterative Golub–Kahan bidiagonalization applied to a factorization of the Calderón operator;
(ii) obtain the first and second derivatives of f via analytic perturbation theory;
(iii) build a piecewise-rational surrogate of f with an AAA-style fitting algorithm constrained by derivatives, which detects and isolates branch points and yields reliable identification of quasi-resonances.