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CNA Seminar
Sivaram Ambikasaran
Courant Institute
Title: Fast algorithms for dense linear algebra

Abstract: Large-dense matrices arise in numerous applications: boundary integral formulation for elliptic partial differential equations, covariance matrices in statistics, inverse problems, radial basis function interpolation, multifrontal solvers for sparse linear systems, etc. As the problem size increases, large memory requirements — scaling as O(N^2) — and extensive computational time to perform matrix algebra— scaling as O(N^2) or O(N^3) — make computations impractical. I will discuss some novel methods for handling these computationally intense problems. In the first half of the talk, I will focus on my innovative algorithm, termed as the Inverse Fast Multipole Method, which permits solving dense linear systems arising out of singular integral equations at a computational cost of O(N). In the second half of the talk, I will discuss my contributions to some of the new developments in handling large dense covariance matrices in the context of computational statistics. More specifically, I will be discussing how fast dense linear algebra (O(N) algorithms for inversion, determinant computation, symmetric factorization, etc.) enables us to handle large scale Gaussian processes and thereby providing an attractive approach for big data applications.

Date: Thursday, October 2, 2014
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer