LANS Informal Seminar: Jie Chen

Seminar Title: Numerical Linear Algebra Challenges in Very Large Scale Data Analysis
Speaker: Jie Chen, Postdoctoral Appointee, MCS

Date/Time: 2011-05-04 15:00
Location: Bldg 240 Conference Center 1404-1405

Description:
With the ever increasing computing power of supercomputers, nowadays computational sciences and engineering demand numerical solutions for problems in a larger and larger scale. One important problem that finds a wide range of applications in such as physical simulations and machine learning, is in a stochastic process the generation of random data from a prescribed covariance rule, and the inverse question of fitting the covariance rule given experimented data. This problem gives rise to a number of numerical linear algebra challenges, where one needs to deal with dense and irregularly structured covariance matrices of mega-, giga- or even much larger sizes. In this talk, I will illustrate specific encountered challenges, including computing the square root of the matrix, estimating the diagonal, solving linear systems, and preconditioning the matrix. For some of these challenges, we have developed efficient and scalable methods that are capable of dealing with matrices of size at least in the mega-scale, on a single desktop machine. As a natural extension, high performance codes run on supercomputers are being developed; however, there remain other unsolved challenging tasks along the line, which call for innovative algorithms as well as theory.