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Haizhao Yang : Data-driven fast algorithms in applied harmonic analysis and numerical linear algebra

Exploring data structures (e.g, periodicity, sparsity, low-rankness) is a universal method in designing fast algorithms in scientific computing. In the first part of this talk, I will show how this idea is applied to the analysis of oscillatory data in applied harmonic analysis. These fast algorithms have been applied to data analysis ranging from materials science, medicine, and art. In the second part, I will discuss how this idea works in some basic numerical linear algebra routines like matrix multiplications and decompositions, with an emphasis in electronic structure calculation.

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