Polynomial eigenvalue decomposition for eigenvalues with unmajorised ground truth – Reconstructing analytic dinosaurs
Schlecht SJ, Weiss S (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 14
Article Number: 100437
DOI: 10.1016/j.sctalk.2025.100437
Abstract
When estimated space-time covariance matrices from finite data, any intersections of ground truth eigenvalues will be obscured, and the exact eigenvalues become spectrally majorised with probability one. In this paper, we propose a novel method for accurately extracting the ground truth analytic eigenvalues from such estimated space-time covariance matrices. The approach operates in the discrete Fourier transform (DFT) domain and groups sufficiently eigenvalues over a frequency interval into segments that belong to analytic functions and then solves a permutation problem to align these segments. Utilising an inverse partial DFT and a linear assignment algorithm, the proposed EigenBone method retrieves analytic eigenvalues efficiently and accurately. Experimental results demonstrate the effectiveness of this approach in reconstructing eigenvalues from noisy estimates. Overall, the proposed method offers a robust solution for approximating analytic eigenvalues in scenarios where state-of-the-art methods may fail.
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Finland (FI)
United Kingdom (GB)How to cite
APA:
Schlecht, S.J., & Weiss, S. (2025). Polynomial eigenvalue decomposition for eigenvalues with unmajorised ground truth – Reconstructing analytic dinosaurs. Science Talks, 14. https://doi.org/10.1016/j.sctalk.2025.100437
MLA:
Schlecht, Sebastian J., and Stephan Weiss. "Polynomial eigenvalue decomposition for eigenvalues with unmajorised ground truth – Reconstructing analytic dinosaurs." Science Talks 14 (2025).
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