Summary: Numer. Math. 46, 213-228 (1985)
@ Springer-Verlag 1985
Regular Splittings and Monotone Iteration Functions
Götz Alefeld and Peter Volkmann
Universität Karlsruhe, Fakultät für Mathematik, Postfach 6380, D-7500 Karlsruhe 1,
Summary. In this paper we introduce the set of so-called monotone iter-
ation functions (MI-functions) belonging to a given function. We prove nec-
essary and sufficient conditions in order that a given MI-function is (in a
precisely defined sense) at least as fast as a second one.
Regular splittings of a function which were initially introduced for lin-
ear functions by R.S. Varga in 1960 are generating MI-functions in a nat-
For linear functions every MI-function is generated by a regular split-
ting. For nonlinear functions, however, this is generally not the case.
Subject Classifications: AMS (MOS): 65115,CR: G1.5.
In his famous book "Matrix Iterative Analysis" Varga [8J has introduced the