In this talk, we will survey some properties of the preconditioners introducedin [1,2] for the solution of the linear systems arising in time-dependent PDEs.Moreover, we will give theoretical results on the convergence rate of the under-lying preconditioned iterations using various Krylov subspace methods. Moreprecisely, if s is the size of the matrices related to the time-step ...

Asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times. This paper reviews certain models of asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains of applications are presented. These include nonsingular linear systems, nonlinear systems, and initial value problems. c © 2000 Elsevier Sci...

Recall that a vector norm on R is a mapping ‖·‖ : R → R satisfying the following conditions: • ‖x‖ > 0 for x 6= 0. • ‖λx‖ = |λ|‖x‖ for x ∈ R and λ ∈ R. • ‖x+ y‖ ≤ ‖x‖+ ‖y‖ for all x, y ∈ R. Since the space Rn×n of all matrices is also a vector space, it is also possible to consider norms there. In contrast to usual vectors, it is, however, also possible to multiply matrices (that is, the matric...

Convergence is a central problem in both computer science and in population biology. Will a program terminate? Will a population go to an equilibrium? In general these questions are quite difficult – even unsolvable. In this paper we will concentrate on very simple iterations of the form

In this talk we will consider three properties of iterations with mixed (finite/countable) supports: iterations of arbitrary length preserve ω1, iterations of length ≤ ω2 over a model of CH have the א2-chain condition and iterations of length < ω2 over a model of CH do not increase the size of the continuum. Definition 1. Let Pκ be an iterated forcing construction of length κ, with iterands 〈Q̇α...

Let f be a smooth self-map of the m-dimensional sphere S. Under the assumption that f preserves latitudinal foliations with the fibres S, we estimate from below the number of fixed points of the iterations of f . The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.

A complete description of the iterated monodromy groups of postcritically finite backward polynomial iterations is given in terms of their actions on rooted trees and automata generating them. We describe an iterative algorithm for finding kneading automata associated with post-critically finite topological polynomials and discuss some open questions about iterated monodromy groups of polynomials.

The behavior of the dynamical zeta function ZD(s) related to several strictly convex disjoint obstacles is similar to that of the inverse Q(s) = 1 ζ(s) of the Riemann zeta function ζ(s). Let Π(s) be the series obtained from ZD(s) summing only over primitive periodic rays. In this paper we examine the analytic singularities of ZD(s) and Π(s) close to the line Rs = s2, where s2 is the abscissa of...