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Advancing Spectral Koopman Methods: ...

Huang, Hung,

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Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms // Hung Huang.
Author:	Huang, Hung,
Description:	1 electronic resource (30 pages)
Notes:	Source: Masters Abstracts International, Volume: 86-07.
Contained By:	Masters Abstracts International86-07.
Subject:	Industrial engineering. -
Online resource:	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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100 1 $a Huang, Hung, $e author. $3 3830346
245 1 0 $a Advancing Spectral Koopman Methods: Challenges in Integrating Randomized Algorithms / $c Hung Huang.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (30 pages)
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500 $a Source: Masters Abstracts International, Volume: 86-07.
500 $a Advisors: Yang, Xiu; Vincente, Luis Nunes.
502 $b M.S. $c Lehigh University $d 2025.
520 $a 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.
546 $a English
590 $a School code: 0105
650 4 $a Industrial engineering. $3 526216
650 4 $a Mathematics. $3 515831
650 4 $a Systems science. $3 3168411
653 $a Koopman analysis
653 $a Randomized algorithms
653 $a Numerical methods
653 $a High-dimensional dynamical systems
690 $a 0546
690 $a 0405
690 $a 0790
710 2 $a Lehigh University. $b Industrial Engineering. $e degree granting institution. $3 3770521
720 1 $a Yang, Xiu $e degree supervisor.
720 1 $a Vincente, Luis Nunes $e degree supervisor.
773 0 $t Masters Abstracts International $g 86-07.
790 $a 0105
791 $a M.S.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31762995