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math.NA2026
Sharp Computational Bounds for Spectral Types of Schrödinger Operators
Matthew J. Colbrook, George Coote
We prove sharp bounds for determining the spectral-type decomposition of Schrödinger operators in the spirit of Smale's program on the foundations of computation. For explicit one-…
math.NA2026
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
George Coote, Matthew J. Colbrook
Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust. A finite EDMD matrix always has eigenvalues; th…