Title:  Cauchy Transforms for Fast and Parallel Matrix Computations

Speaker: Xiaobai Sun, Department of Computer Science, Duke University

Abstract:

I will introduce in this talk a special kind of Cauchy transforms that
can be used as a basic operation for accelerating and parallelizing
matrix computations that arise in existing or emerging applications
with increasingly large data size. Cauchy transforms with interleaving
nodes can be seen as a bridge, in theory and practice, between the
conventional matrix computations using orthogonal transforms and
certain structured matrix computations using the celebrated fast
multipole method~(FMM). They can play the same role as the elementary
orthogonal transforms do in solving linear systems, least squares
regression problems and symmetric eigenvalue problems, which are
intimately related to singular value decompositions~(SVDs). The
advantages are in exploiting the properties of the Cauchy transforms
to enable hierarchical clustering, approximation, preconditiong and
parallelizing matrix computations with an analyzable and
computationally systematic approach. I illustrate their particular use
in designing parallel SVD algorithms.