On multivariable matrix spectral factorization method

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.