Models of parallel chaotic iteration methods
We consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations Ax = b . In the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed. In the second model any processor can update the global approximation which resides in the central processor at any time. This model is a generalization of a sequential iterative scheme due to Ostrowski called the free steering group Jacobi iterative scheme and a chaotic relaxation point iterative scheme due to Chazan and Miranker. We show that when A is a monotone matrix and all the splittings are weak regular, both models lead to convergent schemes.

title: Cone reachability for linear differential systems
abstract: Given a real nxn matrix A and a simplicial cone which is positively invariant under the linear differential system , we consider the problem of characterizing the closure of the set XA(K) of all initial points x(0) ∈ Rn which give rise to solutions x(t) that enter (and remain in) K. An explicit characterization of the closure of XA(K) is given first in case A is diagon-able with a real spectrum. Subsequently a characterization for the closure of XA(K) is given in case there exist k ∈ int K such that −Ak ∈ K, but in the absence of any other explicit assumptions on A.

title: Corrections and additions to: "principal components of minus m-matrices"

title: A combined direct-iterative approach for solving large scale singular and rectangular consistent systems of linear equations
abstract: We construct a certain iterative scheme for solving large scale consistent systems of linear equations Ax = b , (*) where A is a complex m X n matrix of rank r , m ⩾ n , and where A is assumed reasonably well conditioned. The iterative method is obtained through a careful exploitation of an LU -decomposition of A , and, disregarding roundoff errors, it converges to a solution to ( * ), though not necessarily the minimal l 2 -norm one, from any starting vector in r iterations. Moreover, once the LU -decomposition of A is complete, only about r 3 /2 arithmetic operations (multiplications and divisions) are needed to execute the r iterations.

title: A note on generalizations of strict diagonal dominance for real matrices
abstract: We investigate classes of real square matrices possessing some weakened from of strict diagonal dominance of a real matrix whose diagonal entries are all positive. The intersection of each one of these classes with the set of all real matrices, with nonpositive off-diagonal elements, coincides with the set of all nonsingular M - matrices.

title: The Kahan S.O.R. convergence bound for nonsingular and irreducible M-matrices
abstract: Let A be a nonsingular M -matrix, and let π be a block partitioning of A such that the diagonal blocks are square. Denote by J A π and A π ω the block Jacobi and the block S.O.R. iteration matrices arising from and associated with the partitioning π of A , respectively. In  Kahan showed that ρ ( A π ω J A π )]. Under the assumption that J A π is irreducible we examine the question of when ρ( A π ω' )=1 for certain recurring M -matrices.

title: A maximality theorem concerning extreme points

title: On the Strassen disintegration theorem

title: Automatic Continuity of Linear Operators
abstract: The present survey is essentially based on some recent automatic continuity results which have been obtained by Ernst Albrecht and the author in the joint papers [1;2;3]. In contrast to the excellent account of automatic continuity theory in Sinclair's lecture notes [29] and in Dales' recent survey article , the emphasis of the present exposition lies on the automatic continuity problem for linear operators acting between spaces of functions and distributions. The continuity of such operators will be derived from certain conditions which naturally arise in the theory of linear systems, namely from time-invariance and causality on the one side and from dissipativity on the other. The automatic continuity of all time-invariant and causal linear operators turns out to be just one achievement of a far-reaching new theory on automatic continuity which also applies to the problem of continuity for algebrahomomorphisms, derivations, intertwining operators, and local operators. Some central features of this theory will be sketched; in particular, some extensions and variants of the classical principle of uniform boundedness will be discussed.