The factorization of a general matrix into a product of structured factors plays a key role in theoretical and computational linear algebra. In this talk we consider the following question: if we apply one of the standard factorizations to a matrix that is already structured, to what extent do the factors have additional structure related to that of the original matrix? And when such structured factorizations exist, can we develop structure-preserving iterations to compute them?  We will try to provide some answers!

 It is well known that in a problem of minimization of lower  semicontinuous function f  on subsets of Banach space a minimizer may fail to exist. Nevertheless, for some classes of spaces we can prove existence of "small"  functions h such that  the perturbed function  attains its minimum. Traditionally, such results are called variational principles (for example, there are Ekeland's variational principle for metric spaces or Borwein-Preiss variational principle for Hilbert spaces).  In this talk we discuss how Baire category  theorem can be used to prove existence of infinitely many smooth functions h such that f+h attains its minimum. Our presentation is based on  1993 paper by Deville,Godefroy and Zizler.

The classical spaces of holomorphic functions on the unit ball of Cⁿ  are introduced, characterizations of lacunary series which belong to various spaces of holomorphic functions in terms of the Taylor coefficients are given ,some well known results are reviewed and an open problem is also discussed.

SHALL WE BUY AND HOLD ?

Buy good mutual funds and hold on to them is touted by many investment advisors as a sound investment method. We will examine this method using both theoretical analysis and simulation on historical data. Here you can find talk's slides and   a related paper

COMPUTING OPTICAL FLOW

A fundamental problem in the processing of image sequences is the measurement of optical flow (or image velocity). In this talk, I will introduce the concept of optical flow and review various methods for the estimation of optical flow

We continue  our survey of Lagrange stability, Lyapunov stability and asymptotic stability from February 8th. We'll focus on equivalent analytical description of these concepts in terms of Lyapunov functions.  We'll look at analytical properties of Lyapunov functions and their relation to analytical properties of right-hand sides of differential equations and inclusions discussing  classical results and examples  as well as some recent  ones.

We discuss  Lagrange stability  of solutions of differential equations and differential inclusions and characterization of these properties in terms of Lyapunpv functions. This talk presents a review of known results in this field with an emphasis on  converse  Lyapunov function theorems .