Dynamic Mode Decomposition via Polynomial Root-Finding Methods

Dynamic mode decomposition (DMD) is a powerful data-driven tool for analyzing complex systems that has gained significant attention in various scientific and engineering disciplines. It is suitable for the analysis of flow structures in numerical and experimental data, being widely used to extract temporal information about coherent data structures. In this work, we present a novel modification to the standard DMD algorithm by integrating polynomial root-finding methods, enhancing its accuracy and computational efficiency. Our approach leverages iterative techniques for solving polynomial equations to refine the extraction of DMD eigenvalues and DMD modes, resulting in more accurate dynamical reconstructions. We demonstrate the effectiveness of the modified DMD through several case studies, showing the broad scope of applicability of the introduced technique.