On the solution sets of particular classes of linear interval systems

AbstractWe characterize the solution set S of real linear systems Ax=b by a set of inequalities if b lies between some given bounds b̄,b̄ and if the n×n coefficient matrix A varies similarly between two bounds A̱ and Ā. In addition, we restrict A to a particular class of matrices, for instance the class of the symmetric, the skew-symmetric, the persymmetric, the Toeplitz, and the Hankel matrices, respectively. In this way, we generalize the famous Oettli–Prager criterion (Numer. Math. 6 (1964) 405), results by Hartfiel (Numer. Math. 35 (1980) 355) and the contents of the papers (in: R.B. Kearfott, V. Kreinovich (Eds.), Applications of Interval Computations, Kluwer, Boston, MA, 1996, pp. 61–79) and (SIAM J. Matrix Anal. Appl. 18 (1997) 693)

On the existence of a unique solution for a class of nonlinear systems of equations its calculation by iteration methods

summary:Die Arbeit behandelt verschiedene Iterationsverfahren für die Lösung nichtlinearer Gleichungen, welche auf einer Anwendung und gemeinsamer Kombination des Relaxations- und Newtonverfahrens beruhen. Die Methoden werden auch für den Fall einer Intervallarithmetik untersucht. Einige der im Artikel untersuchten Methoden sind auch zur Lösung gewisser Randwertaufgaben geeignet

A REGULARIZED PROJECTION METHOD FOR COMPLEMENTARITY Problems with Non-Lipschitzian Functions

We consider complementarity problems involving functions which are not Lipschitz continuous at the origin. Such problems arise from the numerical solution for differential equations with non-Lipschitzian continuity, e.g. reaction and diffusion problems. We propose a regularized projection method to find an approximate solution with estimation of the error for the non-Lipschitzian complementarity problems. We prove that the projection method globally and linearly converges to a solution of a regularized problem with any regularization parameter. Moreover, we give error bounds for a computed solution of the non-Lipschitzian problem. Numerical examples are presented to demonstrate the efficiency of the method and error bounds