  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.
