On the convergence of asynchronous iteration methods for nonlinear paracontractions and consistent linear systems
The concept of paracontracting operators for fixed point problems and their solution with asynchronous methods was introduced by \textit{L. Elsner, I. Koltracht} and \textit{M. Neumann}, [Numer. Math. 62, No.~3, 305-319 (1992; Zbl 0763.65035)]. The author presents an extension of their results with respect to the properties of the pool of operators from which a common fixed point is searched. As an application of the theory, asynchronous iteration methods for consistent linear systems of equations where the coefficient matrices are singular \(M\)-matrices are considered. The theory of paracontractions and confluence is used for an extension of the results obtained by \textit{B. Lubashevski} and \textit{D. Mitra} [J. Assoc. Comput. Math. 33, No.~1, 130-150 (1986; Zbl 0641.65033)] on asynchronous iteration methods for the Perron-vector problem in the reducible-affine case.
scientific article; zbMATH DE number 1370996