Title: Analysis based fast algorithms for applied mathematics
Speaker: Prof. Sivaram Ambikasaran (Courant Institute of Mathematical Sciences, NYU)
Date: 12 June 2014
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics
The dominant problem in applied mathematics is the application of linear operators and solving linear equations. Dense linear systems arise in numerous applications: Boundary integral equations for elliptic partial differential equations, covariance matrices in statistics, Bayesian inversion, Kalman filtering, inverse problems, radial basis function interpolation, density functional theory, multi-frontal 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, where $N$ is the underlying number of degrees of freedom. This talk will discuss new fast algorithms that scale as $O(N)$ for a class of problems, given a prescribed tolerance. Applications in the context of Gaussian processes, Integral equations for electromagnetic scattering, Symmetric factorization for Brownian dynamics, Bayesian inversion, Kalman filtering, multi-frontal solvers will also be presented.