[BANANA] LAPACK seminar on April 9

[Ming Gu]

               Math 290, Section 16, CS 298, Section 6,
                          Spring 2008
         (Matrix Computations and Scientific Computing)


We meet WEDNESDAYS 11:10 - noon in Room 380 Soda Hall, Berkeley campus.
The coordinators are Profs. J. Demmel (demmel at cs.berkeley.edu), 
M. Gu (mgu at math.berkeley.edu), and B. N. Parlett (parlett at math.berkeley.edu). 
The program will be a mixture of research talks and tutorials.
The tutorials will provide a partial sequel to Math 221.

There will be no seminar next week, which is spring break.
The Bay Area Scientific Computing Day will be on March 29-30, 2008
at the MSRI. You are all welcome to attend.

Date: Apr. 9
Speaker: Thomas Strohmer, UC Davis
Title: The Unreasonable Effectiveness of Banach Algebras in Numerical Analysis

Abstract: I will show that several problems arising at the interface of operator
theory and numerical analysis (including work by Arveson, Gohberg, 
Iserles, Golub, ...) can be solved in an elegant manner by using
concepts from Banach algebra theory. In the first part of my talk 
I will consider the approximate solution of an infinite system of linear 
equations via the classical finite section methods. Using recent results on 
matrix algebras with some form of off-diagonal decay we
will derive qualitative and quantitative convergence results for the finite
section method. We also derive the first finite section method that can be
applied to least squares problems involving a large class of non-hermitian, 
non-Toeplitz-type matrices.

In the second part of my talk I will investigate the interplay of matrix
factorizations and Banach algebras. An important noncommutative
generalization of the famous Wiener's Lemma states that under certain
conditions the inverse $A^{-1}$ of a matrix $A$ will inherit the
off-diagonal decay properties from $A$. I will discuss when this Wiener
property extends to certain matrix factorizations, such as QR-, 
LU-, or polar factorization (but not to the eigenvalue or singular
value decomposition). The fact that these matrix factorizations
have a natural place in the Banach algebra world, allows for a stable
finite-dimensional approximation of these factorization for infinite
matrices. I will discuss applications of the above results to the analysis
of pseudodifferential operators, as well as to signal processing and 
communications.