 Iterative Methods for Computing Eigenvectors of Nonlinear OperatorsGuy Gilboa ()
Chapter 46 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 1631-1657 from Springer Abstract: Abstract In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image processing, graph partition and classification, nonlinear physics, and more. The canonical eigenproblem we solve is T(u) = λu, where T : ℝ n → ℝ n $$T:\mathbb {R}^n\to \mathbb {R}^n$$ is some bounded nonlinear operator. Other variations of eigenvalue problems are also discussed. We present a progression of five algorithms, coauthored in recent years by the author and colleagues. Each algorithm attempts to solve a unique problem or to improve the theoretical foundations. The algorithms can be understood as nonlinear PDEs which converge to an eigenfunction in the continuous time domain. This allows a unique view and understanding of the discrete iterative process. Finally, it is shown how to evaluate numerically the results, along with some examples and insights related to priors of nonlinear denoisers, both classical algorithms and ones based on deep networks. Keywords: Nonlinear spectral analysis; Nonlinear eigenvectors; Spectral total variation; One-homogeneous functoinals. (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_89 Ordering information: This item can be ordered from DOI: 10.1007/978-3-030-98661-2_89 Access Statistics for this chapter More chapters in Springer Books from Springer |
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