Seminar in Numerical Analysis: Guy Gilboa (Technion - Israel Institute of Technology)

A Nonlinear Spectral Analysis of Gradient Flows

Recent studies on nonlinear eigenvalue problems show surprising analogies to harmonic analysis (e.g. Fourier or wavelets). In this talk we first show the total-variation (TV) transform, based on the TV gradient flow, and its application in image processing. We then present new results on analyzing gradient flows of homogeneous nonlinear operators (such as the p-Laplacian). Our framework allows a thorough investigation of Dynamic-Mode-Decomposition (DMD), a central dimensionality reduction method for time series data. We present analytic solutions of simple nonlinear cases, reveal shortcomings of DMD and propose improved decomposition methods.

For further information about the seminar, please visit this webpage.

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