Periodic Multiplicative Algorithms of Selmer Type

Abstract

The multiplicative acceleration of the 2-dimensional Selmer algorithm is considered. Its behavior is more or less unknown and no general result on convergence is known. In this paper we show that periodic expansions do in fact converge and the coordinates of the limit point are rational functions of the largest eigenvalue of the periodicity matrix. Some comparisons are made with the Jacobi-Perron algorithm (Remark1) and the triangle sequence (Section 3).