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Randomized Nyström approximation of non-negative self-adjoint operators
David Persson, Nicolas Boullé, Daniel Kressner
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and stro…
Operator learning without the adjoint
Nicolas Boullé, Diana Halikias, Samuel E. Otto +1
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest th…
On the Convergence of Hermitian Dynamic Mode Decomposition
Nicolas Boullé, Matthew J. Colbrook
We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that appr…
A Mathematical Guide to Operator Learning
Nicolas Boullé, Alex Townsend
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator…
Multivariate rational approximation of functions with curves of singularities
Nicolas Boullé, Astrid Herremans, Daan Huybrechs
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order…