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Journal Articles

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

Spectral Computations

Computing spectral measures of self-adjoint operators
Matthew Colbrook, Andrew Horning, Alex Townsend
SIAM Review, 2021, 63(3), 489-524. (chosen as cover article) pdf journal link
Computing spectral measures and spectral types
Matthew Colbrook*
Communications in Mathematical Physics, 2021, 384, 433-501 pdf journal link
How to compute spectra with error control
(IMA Lighthill-Thwaites Prize Winner 2021)
(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

Follow up article in IMA Mathematics Today: Unscrambling the Infinite: Can we Compute Spectra?
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
Modelling chordwise-varying porosity to reduce aerofoil-turbulence interaction noise
Lorna Ayton, Matthew Colbrook, Thomas Geyer, Paruchuri Chaitanya, Ennes Sarradj
AIAA/CEAS Aeroacoustics, 2021. pdf journal link
Non-linear Forchheimer corrections in acoustic scattering
Matthew Colbrook*, Lorna Ayton
AIAA/CEAS Aeroacoustics, 2021. 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*
pdf
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
Matthew Colbrook*, Vegard Antun, Anders Hansen
arXiv pdf
Computing semigroups with error control
Matthew Colbrook*
pdf
A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations
Matthew Colbrook*, Lorna Ayton
pdf
Stratified sampling based compressed sensing for structured signals
Theresa Loss*, Matthew Colbrook, Anders Hansen
pdf
Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
Dean Johnstone*, Matthew Colbrook*, Anne Nielsen, Patrik Öhberg, Callum Duncan
arXiv


Thesis and Other Publications

The Foundations of Infinite-Dimensional Spectral Computations
Matthew Colbrook
PhD thesis, University of Cambridge, 2020. pdf repository
Unscrambling the Infinite: Can we Compute Spectra?
Matthew Colbrook
IMA Mathematics Today, 2021. pdf journal


Publication Profiles and Code

Google Scholar
Researchgate
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.