Gyurhan Nedzhibov†
This paper introduces an alternative variant of Higher Order Dynamic Mode Decomposition (HODMD), which improves the standard approach from a computational point of view. In the new scheme, timedelayed snapshots are used along with the special form of the Koopman operator. An algorithm is derived that allows the calculation of novel decomposition in a stable and efficient way. This method is suitable in cases where standard Dynamic Mode Decomposition (DMD) is not applicable. These are dynamics that show limited spatial complexity, and a very large number of included frequencies. We illustrate and explain the new method using some classical and sample dynamics.
Keywords: Dynamic Mode Decomposition, DMD, delay embedding, Higher Order DMD, HODMD, Frobenius companion matrix.
MSC: 65P02, 37M02.
DOI https://doi.org/10.56082/annalsarscimath.2024.2.265
†g.nedzhibov@shu.bg Faculty of Mathematics and Informatics, Shumen University Shumen 9700, Bulgaria; paper written with financial support of Shumen University under Grant RD-21-342/01.03.2024
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 2, 2024
