Title :  Cauchy Transforms for Fast and Parallel Matrix Computations

Speaker : Xiaobai Sun
           Department of Computer Science, Duke University

Time :  10:30 AM, Friday, Nov. 11, 2011

Location : ESCB 2120 (Grid Room)
          Department of Computer Science, Old Dominion 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.

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BIO Sketch

Dr. Xiaobai Sun is a Professor of Computer Science at Duke University.
Her research has focused in recent years on fast matrix computations
based on approximation, compression and stability analysis and how to
integrate them on modern computing facilities successfully for
scientific simulations, high-dimensional data analysis and signal and
image processing.  Before joining Duke faculty, she was a postdoctoral
fellow at the Division of Mathematics and Computer Science, Argonne
National Laboratory. She got her PhD in Computer Science, with focus
on numerical computation, from University of Maryland, College Park,
and she got her Master degree in Applied Mathematics in China.