MC
Matthew J. Colbrook
cs.NAmath.NAmath.SPmath.DScs.LGmath.MPmath-phmath.OCmath.APnlin.CD
On Valency
published · living versionsW_g3vccpb6·v1 · currentpublished
From boundary geometry to counterexamples in Smale's mean value problem
with Tom Adamczewski
1 version
W_v8sqks4b·v1published
W_mkpmar6u·v1published
Preprints & journals
58 papers in the corpus · 2015–2026On the planar Neumann--Poincaré inverse spectral problem2610.29661v1 · Habib Ammari, Matthew J. Colbrook2026 · 0 citationsarXivon Valency
Sharp Computational Bounds for Spectral Types of Schrödinger Operators2609.08945v1 · Matthew J. Colbrook, George Coote2026 · 0 citationsarXiv
A counterexample to Kenig's conjecture for the Laplace double-layer operator2609.07947v2 · Matthew J. Colbrook, Siavash Sadeghi2026 · 0 citationsarXiv
The Spectral Skeleton of Chaos: Koopman Wave Packets on Poincaré Sections2609.06565v1 · Jason J. Bramburger, Shiloh-Sheray Gagnon, Rachel Morris et al.2026 · 1 citationarXiv
A Complete Resolution of Forsythe's Conjecture for Restarted Conjugate Gradients2609.04659v2 · Matthew J. Colbrook, George Stepaniants, Alex Townsend2026 · 0 citationsarXiv
A sharp isoperimetric inequality for the Neumann--Poincaré operator in every dimension2608.20466v1 · Matthew J. Colbrook, Siavash Sadeghi2026 · 0 citationsarXiv
A computer-assisted counterexample to the planar Berenstein conjecture2608.08953v1 · Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants2026 · 0 citationsarXiv
A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures2608.01579v1 · Matthew J. Colbrook, George Stepaniants2026 · 0 citationsarXiv
A Proof of the Forsythe Conjecture for the Two-Step Restarted Conjugate Gradient Method2608.02852v1 · Matthew J. Colbrook, George Stepaniants, Alex Townsend2026 · 0 citationsarXiv
Finiteness and exponential growth of full graph -spectra2609.20291v1 · Matthew J. Colbrook2026 · 0 citationsarXiv
No Spectral Invisibility for Dissipative Barrier Truncations in Any Dimension2607.22120v1 · Matthew J. Colbrook, Marco Marletta2026 · 0 citationsarXiv
Nyström Error Beyond -Matrices: A Minimal Diagonally Dominant Obstruction2607.19282v1 · Matthew J. Colbrook2026 · 0 citationsarXiv
Adversarial dynamical systems characterize when data-driven learning succeeds or fails.42448691 · Colbrook, Matthew J, Mezić, Igor, Stepanenko, Alexei2026 · 4 citationsNature communications. 2026;17(1)
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation2606.29083v1 · George Coote, Matthew J. Colbrook2026 · 0 citationsarXiv
PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism2606.27982v1 · Matthew J. Colbrook, April Herwig, J. Nathan Kutz2026 · 0 citationsarXiv
Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems2606.23821v1 · Matthew J. Colbrook2026 · 0 citationsarXiv
Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction2606.09369v1 · Paula Lorenzo-Sanchez, Matthew J. Colbrook, Antonio Navarra2026 · 0 citationsarXiv
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning2606.05131v1 · Kelan Gray, Finlay Brown, Nicolas Boull'e et al.2026 · 0 citationsarXiv
Finding Koopman Invariant Subspaces via Personalized PageRank2605.24666v3 · Hyukpyo Hong, Qin Li, Matthew J. Colbrook et al.2026 · 0 citationsarXiv
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds2603.15091v1 · Gustav Conradie, Nicolas Boull'e, Jean-Christophe Loiseau et al.2026 · 0 citationsarXiv
Computation and Verification of Spectra for Non-Hermitian Systems.41202220 · Drysdale, Catherine, Colbrook, Matthew, Woodley, Michael T M2025 · 1 citationPhysical review letters. 2025;135(17):170202
Avoiding spectral pollution for transfer operators using residuals2507.16915v1 · April Herwig, Matthew J. Colbrook, Oliver Junge et al.2025 · 0 citationsarXiv
Noisy PDE Training Requires Bigger PINNs2507.06967v2 · Sebastien Andre-Sloan, Anirbit Mukherjee, Matthew Colbrook2025 · 0 citationsarXiv
Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms2505.15661v2 · Sina Mohammad-Taheri, Matthew J. Colbrook, Simone Brugiapaglia2025 · 0 citationsarXiv
Universal Methods for Nonlinear Spectral Problems2504.17012v1 · Matthew J. Colbrook, Catherine Drysdale2025 · 0 citationsarXiv
Computing Generalized Eigenfunctions in Rigged Hilbert Spaces2410.08343v1 · Matthew J. Colbrook, Andrew Horning, Tianyiwa Xie2024 · 2 citationsarXiv
Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response2410.01622v2 · Niccolo Zagli, Matthew Colbrook, Valerio Lucarini et al.2024 · 4 citationsarXiv
A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity2408.00845v2 · Catherine Drysdale, Matthew J. Colbrook2024 · 1 citationarXiv
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation2407.20353v2 · Matthew J. Colbrook, Mark Embree, Jake Fillman2024 · 0 citationsarXiv
Multiplicative Dynamic Mode Decomposition2405.05334v2 · Nicolas Boull'e, Matthew J. Colbrook2024 · 4 citationsarXiv
Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators2405.00782v2 · Matthew J. Colbrook, Catherine Drysdale, Andrew Horning2024 · 14 citationsarXiv
Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size2403.05891v1 · Matthew J.Colbrook2024 · 11 citationsarXiv
On the Convergence of Hermitian Dynamic Mode Decomposition2401.03192v2 · Nicolas Boull'e, Matthew J. Colbrook2024 · 1 citationarXiv
The Multiverse of Dynamic Mode Decomposition Algorithms2312.00137v2 · Matthew J. Colbrook2023 · 30 citationsarXiv
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems2308.10697v3 · Matthew J. Colbrook, Qin Li, Ryan V. Raut et al.2023 · 30 citationsarXiv
Avoiding discretization issues for nonlinear eigenvalue problems2305.01691v1 · Matthew J. Colbrook, Alex Townsend2023 · 2 citationsarXiv
Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods2301.02268v2 · Ben Adcock, Matthew J. Colbrook, Maksym Neyra-Nesterenko2023 · 1 citationarXiv
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems2209.02244v1 · Matthew J. Colbrook2022 · 40 citationsarXiv
Residual Dynamic Mode Decomposition: Robust and verified Koopmanism2205.09779v1 · Matthew J. Colbrook, Lorna J. Ayton, M'at'e Szoke2022 · 86 citationsarXiv
The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem.35294283 · Colbrook, Matthew J, Antun, Vegard, Hansen, Anders C2022 · 145 citationsProceedings of the National Academy of Sciences of the United States of America. 2022;119(12):e2107151119
SpecSolve: Spectral methods for spectral measures2201.01314v1 · Matthew J. Colbrook, Andrew Horning2022 · 5 citationsarXiv
Computing spectral properties of topological insulators without artificial truncation or supercell approximation2112.03942v1 · Matthew J. Colbrook, Andrew Horning, Kyle Thicke et al.2021 · 8 citationsarXiv
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems2111.14889v2 · Matthew J. Colbrook, Alex Townsend2021 · 81 citationsarXiv
A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations2111.13070v1 · Matthew J. Colbrook, Lorna J. Ayton2021 · 17 citationsarXiv
WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions2110.12437v1 · Matthew J. Colbrook2021 · 0 citationsarXiv
Computing semigroups with error control2110.06350v1 · Matthew J. Colbrook2021 · 12 citationsarXiv
Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity2107.05635v1 · Dean Johnstone, Matthew J. Colbrook, Anne E. B. Nielsen et al.2021 · 13 citationsPhys. Rev. B 106, 045149 (2022)
On the infinite-dimensional QR algorithm2011.08172v1 · Matthew J. Colbrook, Anders C. Hansen2020 · 16 citationsNumerische Mathematik, 2019, 143(1), 17-83
A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics.33071575 · Colbrook, Matthew J, Kisil, Anastasia V2020 · 15 citationsProceedings. Mathematical, physical, and engineering sciences. 2020;476(2241):20200184
Computing spectral measures of self-adjoint operators2006.01766v2 · Matthew J. Colbrook, Andrew Horning, Alex Townsend2020 · 40 citationsarXiv
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