**Department of Statistics **

Environmental Seminar Series

North Carolina State University
presents

### Arvind Saibaba

FROM Mathematics

FROM NC State University

**Generalized Hybrid Iterative Methods for Large-Scale Inverse Problems**

**Abstract**

Inverse
problems use physical measurements to make inferences about parameters.
We adopt the Bayesian approach for solving inverse problems; however,
this is computationally challenging, especially for large-scale
problems. In this talk, I will discuss recently developed iterative
methods for computing solutions to inverse problems, in which the
parameter-to-observable map is linear. These methods are
particularly useful for large-scale problems where covariance kernels, e.g., those from the Mat'ern class,
are defined on irregular grids and the resulting covariance matrices
are only available via matrix-vector multiplication. Our approach
shares many benefits of standard hybrid methods such as avoiding
semi-convergence and automatically estimating the regularization
parameter. Numerical examples from seismic travel-time tomography and
super-resolution, demonstrate the effectiveness of the described
approaches. I will also discuss some ongoing work on efficiently
computing uncertainty estimates by sampling from the posterior
distribution.

Joint work with Julianne Chung.

**Thursday, 23 March, 2017**

4:30-5:30 pm

**1108 SAS Hall**

Refreshments will be served in the 5th floor commons at 3:45 pm.

__NOTE:__ No food or drink is allowed in any of the classrooms in SAS Hall.