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Session III.1 - Numerical Linear Algebra

Monday, June 19, 16:30 ~ 17:00

Speeding up Krylov subspace methods for matrix functions via randomization

Alice Cortinovis

Stanford University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we consider the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed by forming an orthonormal basis of the Krylov subspace using the Arnoldi method. In this talk, we propose to compute (non-orthonormal) bases in a faster way and to use a fast randomized algorithm for least-squares problems to compute the compression of A onto the Krylov subspace. We present some numerical examples which show that our algorithms can be faster than the standard Arnoldi method while achieving comparable accuracy.

Joint work with Daniel Kressner (EPFL, Switzerland) and Yuji Nakatsukasa (University of Oxford, UK).

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