Further Results on the Convergence of the Pavon-Ferrante Algorithm for Spectral Estimation

TL;DR

This paper rigorously proves that the Pavon-Ferrante fixed-point algorithm for spectral density approximation using Kullback-Leibler divergence globally converges to a fixed point, enhancing understanding of its reliability.

Contribution

It provides the first comprehensive proof of the global convergence of the Pavon-Ferrante spectral estimation algorithm.

Findings

Algorithm globally converges to a fixed point

Enhanced theoretical understanding of spectral estimation methods

Supports reliable application of the algorithm in practice

Abstract

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and Ferrante in [Pavon and Ferrante, 2006]. Our main result states that the algorithm globally converges to one of its fixed points.