2662369
CONVERGENCE OF INFINITE PRODUCTS OF MATRICES AND INNER{OUTER ITERATION SCHEMES
We develop conditions under which a product Q1=0 Ti of matrices chosen from a possibly innite set of matricesS =fTjjj2 Jg converges. We obtain the following conditions which are sucient for the convergence of the product: There exists a vector norm such that all matrices in S are nonexpansive with respect to this norm and there exists a subsequencefikg 1=0 of the sequence of the nonnegative integers such that the corresponding sequence of operators Tik 1=0 converges to an operator which is paracontracting with respect to this norm. We deduce the continuity of the limit of the product of matrices as a function of the sequencesfikg1=0 . But more importantly, we apply our results to the question of the convergence of inner{outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.
121745003
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 [5] 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.
121748192
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.
120746270
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.
122147649
Cone reachability for linear differential systems
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.
18512153
Algorithms for Computing Bases for the Perron Eigenspace with PrescribedNonnegativity and Combinatorial Properties
Let $P$ be an $n \times n$ nonnegative matrix. In this paper the authors introduce a method called the SCANBAS algorithm for computing a union of (Jordan) chains $\cal{C}$ corresponding to the Perron eigenvalue of $P$, such that $\cal{C}$ consists of nonnegative vectors only and such that at each height, $\cal{C}$ contains the maximal number of nonnegative vectors of that height possible in a height basis for the Perron eigenspace of $P$. It is further shown that $\cal{C}$ can be extended to a height basis for the Perron eigenspace of $P$. The chains are extracted from transform components of $P$ that are, in turn, polynomials in $P$. When the Perron eigenspace has a Jordan basis consisting of nonnegative vectors only, this algorithm computes such a basis. The paper concludes with various examples computed by the algorithm using MATLAB. The work here continues and deepens work on computing nonnegative bases for the Perron eigenspace from polynomials in the matrix already begun by Hartwig, Neumann, and Rose and by Neumann and Schneider.
122751787
Varianten zum Konvergenzsatz von Simons und Anwendungen in der Choquettheorie
122589104
Bemerkungen zum von Neumannschen Minimaxtheorem
118524160
Automatic Continuity of Linear Operators
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 [9], 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.
123207765
On the Strassen disintegration theorem
120206552
Beschränktheitsaussagen für sublineare und bisublineare Funktionale