On the Convergence of a Matricial Fixed-Point Iteration Connected with Spectral Estimation. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Baggio, Giacomo
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 7415
• Page End: 7420
• Publication Date: 2017-07
• Subjects: Stability of nonlinear systems -- Lyapunov methods -- Application of nonlinear analysis -- design -- Convergence analysis -- Fixed-point iteration -- Spectral density estimation; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.1499
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, an in-depth analysis of a nonlinear matricial fixed-point iteration and its convergence properties is provided. Remarkably, the analyzed iteration can be regarded as a "frequency-sampled" version of a thoroughly investigated and very efficient fixed-point iteration for Kullback–Leibler approximation of spectral densities, proposed in Pavon and Ferrante (2006). A proof of global convergence to a prescribed set of fixed points of the latter iteration seems to be elusive, though conjectured and corroborated by an extensive campaign of numerical simulations (Ferrante et al., 2011). The present work represents a first step towards the solution of this conjecture.