Sequences of Problems, Matrices, and Solutions

Eric de Sturler of Virginia Tech Department of Mathematics presented a lecture on November 12, 2010 at 2:00 pm in room 1447 of the Klaus Advanced Computing Building on the Georgia Tech campus.Eric de Sturler received his PhD in 1994 at Delft University of Technology under the supervision of Henk van der Vorst. From 1993, he spent 5 years at ETH Zurich as (senior) research scientist at the Interdisciplinary Project Center for Supercomputing and the Swiss Center for Scientific Computing. He was a Leslie Fox prizewinner in 1997, and he spent the summer of 1997 visiting Stanford University at the invitation of Prof. Gene Golub. In 1998, he joined the faculty of the Department of Computer Science at the University of Illinois at Urbana-Champaign. He has been on faculty of the Mathematics Department at Virginia Tech since 2006. He was the Program Director of the SIAM Activity Group on Supercomputing from 2003 to 2006; he co-chaired the third SIAM Conference on Computational Science and Engineering in 2005; he is a general co-chair of the 13th IEEE International Conference on Computational Science and Engineering in 2010; and he is on the organizing committee of the SIAM Conference on Applied Linear Algebra in 2012. He has served as an editor for multiple journals, among others, for Applied Numerical Mathematics since 2005 and for SIAM Journal on Numerical Analysis from 2003 to 2009.Runtime: 56:14 minutesIn a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions