On multivariable matrix spectral factorization method

TL;DR

This paper extends the Janashia-Lagvilava algorithm to multivariable matrix spectral factorization, providing a new numerical method for solving this complex problem with practical applications.

Contribution

The paper introduces a novel extension of the Janashia-Lagvilava algorithm to multivariable cases, enabling effective numerical spectral factorization.

Findings

Developed a new numerical algorithm for multivariable spectral factorization.

Demonstrated the algorithm's effectiveness in practical applications.

Extended existing methods to handle multivariable cases.

Abstract

Spectral factorization is a prominent tool with several important applications in various areas of applied science. Wiener and Masani proved the existence of matrix spectral factorization. Their theorem has been extended to the multivariable case by Helson and Lowdenslager. Solving the problem numerically is challenging in both situations, and also important due to its practical applications. Therefore, several authors have developed algorithms for factorization. The Janashia-Lagvilava algorithm is a relatively new method for matrix spectral factorization which has proved to be useful in several applications. In this paper, we extend this method to the multivariable case. Consequently, a new numerical algorithm for multivariable matrix spectral factorization is constructed.