Dynamic mode decomposition (DMD) is a data-driven, modal decomposition technique that describes spatiotemporal features of high-dimensional dynamic data. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations. The main purpose of this article is to introduce new alternatives to the currently accepted algorithm for calculating the dynamic mode decomposition. We present two new algorithms which are more economical from a computational point of view, which is an advantage when working with large data. With a few illustrative examples, we demonstrate the applicability of the introduced algorithms.

We present novel methods for computing the online dynamic mode decomposition (online DMD) for streaming datasets. We propose a framework that allows incremental updates to the DMD operator as data become available. Due to its ability to work on datasets with lower ranks, the proposed method is more advantageous than existing ones. A noteworthy feature of the method is that it is entirely data-driven and does not require knowledge of any underlying governing equations. Additionally, we present a modified version of our proposed approach that utilizes a weighted alternative to online DMD. The suggested techniques are demonstrated using several numerical examples.

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Dynamic mode decomposition (DMD) is a data-driven mathematical technique to extract spectral information from complex data coming from numerical or experimental studies of various systems. It is an equation-free method in the sense that it does not require knowledge of the underlying governing equations. In this article we explore and demonstrate a new algorithm for calculating the DMD decomposition.