130 citations · 345 across the 38 of their papers we have counts for
7 papers · 1 filter
Computing spectral properties of topological insulators without artificial truncation or supercell approximation
Matthew J. Colbrook, Andrew Horning, Kyle Thicke +1
Topological insulators (TIs) are renowned for their remarkable electronic properties: quantised bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in…
A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations
Matthew J. Colbrook, Lorna J. Ayton
We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable…
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
Matthew J. Colbrook, Alex Townsend
Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. How…
WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions
Matthew J. Colbrook
Reconstruction of signals from undersampled and noisy measurements is a topic of considerable interest. Sharpness conditions directly control the recovery performance of restart sc…
Computing semigroups with error control
Matthew J. Colbrook
We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator , a time , an arb…
Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
Dean Johnstone, Matthew J. Colbrook, Anne E. B. Nielsen +2
Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum…
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
Matthew J. Colbrook, Vegard Antun, Anders C. Hansen
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when…