The Janashia–Lagvilava Method of Matrix Spectral Factorization: Recent Advances and Exponential Acceleration

by Prof. Lasha Ephremidze (Kutaisi International University and Razmadze Mathematical Institute)

Friday Jun 26, 2026, 3:15 PM → 4:15 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

Abstract:

Matrix spectral factorization is a classical problem with numerous applications in prediction theory, control engineering, signal processing, communications, and mathematical physics. While several computational approaches have been developed over the past decades, reliable factorization of large-scale or nearly singular matrix functions remains a challenging task.

In this talk, I will present the Janashia–Lagvilava method of matrix spectral factorization, originally developed at the A. Razmadze Mathematical Institute. The method is based on a recursive reduction of the matrix factorization problem to a sequence of scalar spectral factorizations and has been shown to possess strong numerical stability properties, particularly in situations where traditional algorithms encounter difficulties.

After reviewing the main ideas behind the method and its theoretical foundations, I will discuss several recent developments, including a new non-commutative reformulation of the algorithm, which leads to an exponential acceleration of the computational procedure. Numerical experiments demonstrate dramatic performance improvements for large-scale matrix functions while preserving the robustness and accuracy of the original method.

The results illustrate how classical ideas from harmonic analysis can be combined with modern computational techniques to address contemporary challenges in large-scale data analysis.