Title :
Consequences of a properly implemented computer arithmetic for periodicities of iterative methods
Author :
Klatte, R. ; Ullrich, Ch.
Abstract :
In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer arithmetic is properly implemented.
Keywords :
Computers; Digital arithmetic; Finite element methods; Indexes; Iterative methods; Vectors; Zirconium; Rounding invariant structures; cycle; floating-point arithmetic; weakly cyclic vector function;
Conference_Titel :
Computer Arithmetic (ARITH), 1975 IEEE 3rd Symposium on
Conference_Location :
Dallas, TX, USA
DOI :
10.1109/ARITH.1975.6156992
