123146090
Corrections and additions to: "principal components of minus 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.
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.
120901930
Nonnegative jordan bases
In this paper we are concerned with the problem of when the generalized eigenspace of an n × n nonegative matrix A corresponding to its spectrai radius ρ has a nonnegative Jordan basis. Richman and Schneider have shown this to hold when, and only when, the Weyr characteristics of A corresponding to ρ is equal to the vector of levels in the singular graph of A Here we develop sufficient conditions for this equality to hold based upon the linear independence of a certain set of vectors which are generated according to a process of elimination of totally independent chains from the singular graph. We show that this condition comes close to being a further characterization for the existence of a nonnegative Jordan basis for this eigenspace and actually conjecture that this is the case. Finally, we show that this eigenspace has a Rothblum basis which is a Jordan basis if and only if the singular graph is a disjoint union of chains.
121609264
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.
120206552
Beschränktheitsaussagen für sublineare und bisublineare Funktionale
122589104
Bemerkungen zum von Neumannschen Minimaxtheorem
121595993
Continuity of sublinear operators on F-spaces
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.
120497198
A maximality theorem concerning extreme points
122751787
Varianten zum Konvergenzsatz von Simons und Anwendungen in der Choquettheorie