 
Summary: Numer. Math. 46, 213228 (1985)
Numerische
Mathematik
@ SpringerVerlag 1985
Regular Splittings and Monotone Iteration Functions
Götz Alefeld and Peter Volkmann
Universität Karlsruhe, Fakultät für Mathematik, Postfach 6380, D7500 Karlsruhe 1,
Bundesrepublik Deutschland
Summary. In this paper we introduce the set of socalled monotone iter
ation functions (MIfunctions) belonging to a given function. We prove nec
essary and sufficient conditions in order that a given MIfunction 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 MIfunctions in a nat
ural manner.
For linear functions every MIfunction 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.
o. Introduction
In his famous book "Matrix Iterative Analysis" Varga [8J has introduced the
