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Journal Articles

(*denotes first authors where applicable, others alphabetical)
(paper prizes shown in orange)

Spectral Computations

Computing spectral measures of self-adjoint operators
Matthew Colbrook, Andrew Horning, Alex Townsend
SIAM Review, to appear. pdf
Computing spectral measures and spectral types
Matthew Colbrook*
Communications in Mathematical Physics, 2021. pdf journal link
How to compute spectra with error control
(Smith-Knight/Rayleigh-Knight Prize Class I 2018)
Matthew Colbrook*, Bogdan Roman, Anders Hansen
Physical Review Letters, 2019, 122(25), 250201. (chosen as cover article) pdf journal link
On the infinite-dimensional QR algorithm
Matthew Colbrook*, Anders Hansen
Numerische Mathematik, 2019, 143(1), 17-83. pdf journal link
Pseudoergodic operators and periodic boundary conditions
Matthew Colbrook*
Mathematics of Computation, 2020, 89(322), 737-766. pdf journal link

Spectral Methods

A Mathieu function boundary spectral method for diffraction by multiple variable poro-elastic plates, with applications to metamaterials and acoustics
Matthew Colbrook*, Anastasia Kisil
Proceedings of the Royal Society A, 2020, 476(2241), 20200184. pdf journal link
The unified transform for mixed boundary condition problems in unbounded domains
(IMA Lighthill-Thwaites Prize Finalist 2019)
Matthew Colbrook*, Lorna Ayton, Athanassios Fokas
Proceedings of the Royal Society A, 2019, 475(2222), 20180605. pdf journal link
Extending the unified transform: curvilinear polygons and variable coefficient PDEs
Matthew Colbrook*
IMA Journal of Numerical Analysis, 2020, 40(2), 976-1004. pdf journal link
A hybrid analytical-numerical technique for elliptic PDEs
Matthew Colbrook*, Thanasis Fokas, Parham Hashemzadeh
SIAM Journal on Scientific Computing, 2019, 41(2), A1066-A1090. pdf journal link
On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains
Matthew Colbrook*, Natasha Flyer, Bengt Fornberg
Journal of Computational Physics, 2018, 374, 996-1016. pdf journal link

Numerical Solution of Scattering Problems

Do we need non-linear corrections? On the boundary Forchheimer equation in acoustic scattering
Matthew Colbrook*, Lorna Ayton
Journal of Sound and Vibration, 2021, 495, 115905. pdf journal link
Reducing aerofoil-turbulence interaction noise through chordwise-varying porosity
Lorna Ayton*, Matthew Colbrook, Thomas Geyer, Paruchuri Chaitanya, Ennes Sarradj
Journal of Fluid Mechanics, 2020, 906, p. A1. DOI: 10.1017/jfm.2020.746. pdf journal link
Fast and spectrally accurate numerical methods for perforated screens
(with applications to Robin boundary conditions)

Matthew Colbrook, Matthew Priddin
IMA Journal of Applied Mathematics, 2020, 85(5), 790-821. pdf journal link
A spectral collocation method for acoustic scattering by multiple elastic plates
Matthew Colbrook*, Lorna Ayton
Journal of Sound and Vibration, 2019, 461, 114904. pdf journal link

Computational Fluid Mechanics

A hybrid analytical-numerical method for solving advection-dispersion problems on a half-line
Felipe de Barros, Matthew Colbrook, Athanassios Fokas
International Journal of Heat and Mass Transfer, 2019, 139, 482-491. pdf journal link
Scaling laws of passive-scalar diffusion in the interstellar medium
Matthew Colbrook*, Xiangcheng Ma, Philip Hopkins, Jonathan Squire
Monthly Notices of the Royal Astronomical Society, 2017, 467(2), 2421-2429. pdf journal link

Computation and Analysis of PDEs

Kernel density estimation with linked boundary conditions
Matthew Colbrook*, Zdravko Botev, Karsten Kuritz, Shev MacNamara
Studies in Applied Mathematics, 2020, 145(3), 357-396. pdf journal link

Refereed Conference Articles

On the existence of stable and accurate neural networks for image reconstruction
Matthew Colbrook*, Vegard Antun, Anders Hansen
Signal Processing with Adaptive Sparse Structured Representations (SPARS), 2019. pdf journal link
The unified transform: a spectral collocation method for acoustic scattering
Lorna Ayton, Matthew Colbrook, Athanassios Fokas
AIAA/CEAS Aeroacoustics, 2019. pdf journal link

Selected Submitted Articles/Preprints

The foundations of spectral computations via the solvability complexity index hierarchy: Part I
Matthew Colbrook*, Anders Hansen
arXiv pdf
On the computation of geometric features of spectra of linear operators on Hilbert spaces
Matthew Colbrook*
Computing Spectra - On the solvability complexity index hierarchy and towers of algorithms
Jonathan Ben-Artzi, Matthew Colbrook, Anders Hansen, Olavi Nevanlinna, Markus Seidel
arXiv pdf
Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem
Vegard Antun, Matthew Colbrook, Anders Hansen
arXiv pdf
Computing semigroups with error control
Matthew Colbrook*
Stratified sampling based compressed sensing for structured signals
Theresa Loss*, Matthew Colbrook, Anders Hansen

Publication Profiles and Code

Google Scholar
Some of my code can be found on my GitHub profile.
Code for \(\texttt{SpecSolve}\) can be found here.
Code for \(\texttt{FIRENETs}\) can be found here.