Neighborhoods of dominant convergence for the SSOR method
Let A be an $n \times n$ nonsingular irreducible 3-cyclic H-matrix and let $J^A$, $L_\omega ^A$ and $S_\omega ^A $ denote, respectively, the Jacobi, the SOR, and the SSOR iteration matrices associated with A. In this paper we show that if the spectral radius $\rho ( | J^A | ) \in ( 0,r_0 )$, where $r_0$ is the unique root of the cubic $17r^3 + r^2 - r - 1$ in the interval (0, 1), then there exists a neighborhood $\Omega _{\omega ( A )} $ of $\omega ( A ) : = 2 /( 1 + \rho ( | J^A | )$ such that \[ \rho ( S_\omega ^A ) < | \omega - 1 | \leqq \rho ( L_\omega ^A )\quad \forall \omega \in \Omega _{\omega ( A )} .

title: On the square roots of strictly quasiaccretive complex matrices
abstract: The square roots of a complex n × n matrix A for which the real part of e ix A , where χϵ[ −π 2 , π 2 ] , is positive definite are investigated. It is shown, for example, that when χ= −π 2 (i.e., A is strictly dissipative), A has a unique square root whose real and imaginary parts are both positive definite.

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

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: On the Strassen disintegration theorem

title: A maximality theorem concerning extreme points

title: Continuity of sublinear operators on F-spaces
abstract: In this note, some of the fundamental theorems concerning the automatic continuity of positive linear functionals and positive linear operators (see [9,14,21]) as well as certain uniform boundedness type theorems (see [5,13,15,19]) will be extended to derive various continuity properties of (even discontinuous) sublinear operators from some metrizable topological vector space to some ordered topological vector space.

title: Beschränktheitsaussagen für sublineare und bisublineare Funktionale

title: Varianten zum Konvergenzsatz von Simons und Anwendungen in der Choquettheorie