Paper#Dynamical Systems, Koopman Operator, Spectral Analysis, Data-Driven Methods🔬 ResearchAnalyzed: Jan 3, 2026 06:39
Data-Driven Spectral Analysis with Pseudo-Resolvent Koopman Operator
Published:Dec 31, 2025 16:33
•1 min read
•ArXiv
Analysis
This paper introduces a data-driven method to analyze the spectrum of the Koopman operator, a crucial tool in dynamical systems analysis. The method addresses the problem of spectral pollution, a common issue in finite-dimensional approximations of the Koopman operator, by constructing a pseudo-resolvent operator. The paper's significance lies in its ability to provide accurate spectral analysis from time-series data, suppressing spectral pollution and resolving closely spaced spectral components, which is validated through numerical experiments on various dynamical systems.
Key Takeaways
- •Presents a data-driven method for spectral analysis of the Koopman operator.
- •Addresses spectral pollution in finite-dimensional approximations.
- •Constructs a pseudo-resolvent operator using the Sherman-Morrison-Woodbury identity.
- •Demonstrates effectiveness in suppressing spectral pollution and resolving closely spaced spectral components.
- •Provides convergence guarantees and error bounds for eigenvalue approximation.
Reference
“The method effectively suppresses spectral pollution and resolves closely spaced spectral components.”