DEIM
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Related Articles from SNS
Low-Rank Acceleration of the Operator Fourier Transform
arXiv:2606.09689v1 Announce Type: new Abstract: We develop a numerical algorithm for the efficient solution or approximation of solutions to the Helmholtz equation on a structured grid in two dimensions. We make use of the Operator Fourier Transform (OFT) and a low-rank cross approximation scheme (Cross-DEIM) to decompose the problem into an integral over a pseudo-time of solutions to the Schr\"odinger equation. The OFT is a framework for solving operator equations like fractional Laplacian...
Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
arXiv:2502.02718v2 Announce Type: replace Abstract: The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-DEIM projection ROMs with various strategies for parameter sampling and snapshot collection. The aim is to identify an approach for constructing a ROM that is efficient across a range of parameters, encompassing several regimes exhibited by the KS and gKS...
Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection
arXiv:2510.20116v2 Announce Type: replace Abstract: This work investigates the reduction of phasor measurement unit (PMU) data through low-rank matrix approximations. To reconstruct a PMU data matrix from fewer measurements, we propose the framework of interpolatory matrix decompositions (IDs). In contrast to methods relying on principal component analysis or singular value decomposition, IDs recover the complete data matrix using only a few of its rows (PMU datastreams) and/or a few of its...