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Session III.1 - Numerical Linear Algebra

Wednesday, June 21, 15:30 ~ 16:00

Randomized matrix-free quadrature

Tyler Chen

New York University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We discuss randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied are characterized by the use of a Krylov subspace method to approximate independent and identically distributed samples of $\mathbf{v}^*f(\mathbf{A})\mathbf{v}$, where $\mathbf{v}$ is an isotropic random vector, $\mathbf{A}$ is a Hermitian matrix, and $f(\mathbf{A})$ is a matrix function. This class of algorithms includes the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for approximating spectra and spectral sums. We will provide a unified framework for understanding these algorithms, and provide examples which shed light on the commonalities and tradeoffs between them.

Joint work with Thomas Trogdon (University of Washington) and Shashanka Ubaru (IBM Watson).

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