On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains. - Matthew J. Colbrook; Natasha Flyer; Bengt Fornberg (J. Comput. Phys., 2018)

Computing Spectral Measures and Spectral Types: New Algorithms and Classifications. - Matthew John Colbrook (CoRR, 2019)

On the infinite-dimensional QR algorithm. - Matthew J. Colbrook; Anders C. Hansen (Numerische Mathematik, 2019)

A Hybrid Analytical-Numerical Technique for Elliptic PDEs. - Matthew J. Colbrook; Thanasis Fokas; Parham Hashemzadeh (SIAM J. Sci. Comput., 2019)

Pseudoergodic operators and periodic boundary conditions. - Matthew J. Colbrook (Math. Comput., 2020)

Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem. - Vegard Antun; Matthew J. Colbrook; Anders C. Hansen (CoRR, 2021)

WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions. - Matthew J. Colbrook (CoRR, 2021)

Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems. - Matthew J. Colbrook; Alex Townsend (CoRR, 2021)

Computing spectral properties of topological insulators without artificial truncation or supercell approximation. - Matthew J. Colbrook; Andrew Horning; Kyle Thicke; Alexander B. Watson (CoRR, 2021)

Computing Spectral Measures of Self-Adjoint Operators. - Matthew J. Colbrook; Andrew J. Horning; Alex Townsend (SIAM Rev., 2021)

SpecSolve: Spectral methods for spectral measures. - Matthew J. Colbrook; Andrew Horning (CoRR, 2022)

Residual Dynamic Mode Decomposition: Robust and verified Koopmanism. - Matthew J. Colbrook; Lorna J. Ayton; Máté Szoke (CoRR, 2022)

A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations. - Matthew J. Colbrook; Lorna J. Ayton (J. Comput. Phys., 2022)

Computing Semigroups with Error Control. - Matthew J. Colbrook (SIAM J. Numer. Anal., 2022)

Stratified Sampling Based Compressed Sensing for Structured Signals. - Theresa Loss; Matthew J. Colbrook; Anders C. Hansen (IEEE Trans. Signal Process., 2022)

WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for Inverse Problems with Approximate Sharpness Conditions. - Matthew J. Colbrook (SIAM J. Imaging Sci., 2022)

Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods. - Ben Adcock; Matthew J. Colbrook; Maksym Neyra-Nesterenko (CoRR, 2023)

Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems. - Matthew J. Colbrook; Qin Li; Ryan V. Raut; Alex Townsend (CoRR, 2023)

The Multiverse of Dynamic Mode Decomposition Algorithms. - Matthew J. Colbrook (CoRR, 2023)

The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems. - Matthew J. Colbrook (SIAM J. Numer. Anal., 2023)

On the Convergence of Hermitian Dynamic Mode Decomposition. - Nicolas Boullé; Matthew J. Colbrook (CoRR, 2024)

Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size. - Matthew J. Colbrook (CoRR, 2024)

Limits and Powers of Koopman Learning. - Matthew J. Colbrook; Igor Mezic; Alexei Stepanenko (CoRR, 2024)

Optimal Algorithms for Quantifying Spectral Size with Applications to Quasicrystals. - Matthew J. Colbrook; Mark Embree; Jake Fillman (CoRR, 2024)

A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity. - Catherine Drysdale; Matthew J. Colbrook (CoRR, 2024)

Computing Generalized Eigenfunctions in Rigged Hilbert Spaces. - Matthew J. Colbrook; Andrew J. Horning; Tianyiwa Xie (CoRR, 2024)

On the Computation of Geometric Features of Spectra of Linear Operators on Hilbert Spaces. - Matthew J. Colbrook (Found. Comput. Math., 2024)

Multiplicative Dynamic Mode Decomposition. - Nicolas Boullé; Matthew J. Colbrook (SIAM J. Appl. Dyn. Syst., 2025)

Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators. - Matthew J. Colbrook; Catherine Drysdale; Andrew Horning (SIAM J. Appl. Dyn. Syst., 2025)

Avoiding Discretization Issues for Nonlinear Eigenvalue Problems. - Matthew J. Colbrook; Alex Townsend (SIAM J. Matrix Anal. Appl., 2025)

Universal Methods for Nonlinear Spectral Problems. - Matthew J. Colbrook; Catherine Drysdale (CoRR, 2025)

Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms. - Sina Mohammad-Taheri; Matthew J. Colbrook; Simone Brugiapaglia (CoRR, 2025)

Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces. - Nicolas Boullé; Matthew J. Colbrook; Gustav Conradie (CoRR, 2025)

Avoiding spectral pollution for transfer operators using residuals. - April Herwig; Matthew J. Colbrook; Oliver Junge; Péter Koltai; Julia Slipantschuk (CoRR, 2025)