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Plenary talk

Monday, June 19, 9:30 ~ 10:30

Randomization for solving difficult linear algebra problems

Daniel Kressner

EPFL, Switzerland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Randomized algorithms are becoming increasingly popular in matrix computations. Recent software efforts, such as RandLAPACK, testify that randomization is on the brink of replacing existing deterministic techniques for several large-scale linear algebra tasks. The poster child of these developments, the randomized singular value decomposition is nowadays one of the state-the-of-art approaches for performing low-rank approximation. In this talk, we will discuss numerous further examples for the potential of randomization to facilitate the solution of notoriously difficult linear algebra tasks. This includes a simple numerical algorithm for jointly diagonalizing a family of nearly commuting matrices, the solution of challenging singular and nonlinear eigenvalue problems, as well as the low-rank approximation of matrix functions and matrix-valued functions. A common theme of all these developments is that randomization helps turn linear algebra results that only hold generically into robust and reliable numerical algorithms.

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