A matrix map F (x) is said to be (matricially) convex, if u T F (x)u is a convex function for every u. In this paper, semideenite systems of the type F (x) 0, where F (x) is ma-tricially convex, are considered. This class of problems generalizes both aane semideenite inequalities as well as ordinary convex inequality systems. After establishing characterizations and properties of matricial conv...

The Sznajd model in less than a year has found several followers. An isolated person does not convince others; a group of people sharing the same opinions influences the neighbours much more easily. Thus on a square lattice, with variables +1 (Democrats) and –1 (Republicans) on every lattice site, a pair (or plaquette) of neighbours convinces its six (eight) nearest neighbours of its own opinio...

This paper is concerned with the approximate solution of a functional differential equation of the form: x′(t) = α(t)x(t)+β (t)x(t−1)+ γ(t)x(t +1). (1) We search for a solution x, defined for t ∈ [−1,k],(k ∈ IN), which takes given values on the intervals [−1,0] and (k− 1,k]. Continuing the work started in [10], we introduce and analyse some new computational methods for the solution of this pro...

The renormalization of a quadratic-like map is studied. The threedimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the a priori complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan’s sector theorem is discussed and i...

The tetrahedral finite element approximation of the Stokes problem is analyzed by means of polynomials piecewise of degree k +1 for the velocity and continuous piecewise of degree k for the pressure. A stability result is given for every k ≥ 1.

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi-Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. It is shown that this JDSVD method can be seen as an accelerated (inexact) Newton scheme. We compare the method with...

A semi-implicit, lowest order finite element scheme for the approximation of wave maps into smooth or convex surfaces is devised and its stability is analyzed. Convergence is established for the case of the unit sphere as a target manifold, which is unconditional in case of (2+1) Minkowski space. Numerical experiments illustrate the theoretical results.

A Newton-like method for convex functions is derived. It is shown that this method can be better than the Newton method. Especially good results can be obtained if we combine these two methods. Illustrative numerical examples are given. Mathematics Subject Classification: 65H05

Abstract: The aim of this work is to introduce an adaptive strategy to monitor the rate of convergence of a Newton-like method in numerical shape optimization. Such superlinear iterative algorithms are often computationally intensive and the rate of convergence depends on how accurate the numerical solution of the state equation is. The model concerns a cost function depending on the unknown do...