A NEW CHARACTERIZATION OF M-MATRIX AND APPLICATIONS
P. Spitéri · 1994
The notion of accretive operator (see [1], [2]) plays an important part in the study of nonlinearsemigroups. According to this notion, we set up in the present study, essential properties of accretivity which allow to connect the set of linear accretive operators dened in a nite dimensional space with the set of M-matrix (see [3]). Such results allow us on one hand to make a link between various notions arising in nonlinear analysis and linear algebra and on the other hand to generalize some preliminaries results obtained in the characterization by accretive matrices of diagonally dominant matrices with positive diagonal entries (see [5], [4]). The previous result allows us to study two distinct kinds of applications : - the rst application concerns the convergence analysis of asynchronous subdomain methods for the solution of nonlinear boundary value problems, - the second application concerns the Liapounov stability analysis of linear or some particular nonlinear evolution systems.