Iterative Methods for Computing Eigenvectors of Nonlinear Operators

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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: Rn → Rn 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.

Original languageEnglish
Title of host publicationHandbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Subtitle of host publicationMathematical Imaging and Vision
Number of pages27
ISBN (Electronic)9783030986612
StatePublished - 1 Jan 2023


  • Nonlinear eigenvectors
  • Nonlinear spectral analysis
  • One-homogeneous functoinals
  • Spectral total variation

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science


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