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Advancing Spectral Koopman Methods: ...

Huang, Hung,

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Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms // Hung Huang.
作者:	Huang, Hung,
面頁冊數:	1 electronic resource (30 pages)
附註:	Source: Masters Abstracts International, Volume: 86-07.
Contained By:	Masters Abstracts International86-07.
標題:	Industrial engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31762995
ISBN:	9798302178343

Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms /
Huang, Hung,

Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms /Hung Huang. - 1 electronic resource (30 pages)

Source: Masters Abstracts International, Volume: 86-07.

This thesis investigates the potential enhancement of the Sparse-Grid-Based Adaptive Spectral Koopman (SASK) method through the integration of modern randomized algorithms. Specifically, this research examines the transition from MATLAB's standard eig function to the more efficient eigs implementation, followed by an attempted integration with the sketched Rayleigh-Ritz (sRR) method. While the eigs implementation demonstrates substantial performance improvements-achieving up to 68 times faster computation while maintaining solution accuracy-the integration of sRR reveals fundamental compatibility challenges due to eigenvalue classification requirements in Koopman analysis. These findings provide crucial insights into the mathematical constraints of enhancing Koopman operator methods with randomized algorithms, contributing to the ongoing development of efficient numerical methods for high-dimensional dynamical systems.

English

ISBN: 9798302178343Subjects--Topical Terms:

526216
Industrial engineering.
Subjects--Index Terms:

Koopman analysis

Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms /
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