Weak convergence of the periodic multiplicative Selmer algorithm

TL;DR

This paper proves the weak convergence of the periodic multiplicative Selmer algorithm by analyzing the properties of its periodicity matrix and eigenvalues, establishing key relations for the convergence proof.

Contribution

It introduces a method to demonstrate weak convergence by linking the periodicity matrix's positivity and eigenvalue relations.

Findings

Established positivity of the periodicity matrix.

Derived relations between matrix entries and eigenvalues.

Proved the existence of limits leading to convergence.

Abstract

In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these relations exist, we arrive at the desired result.