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Scaled Relative Graph of Normal Matrices

Numerical Analysis 2024-12-05 v3 Numerical Analysis Optimization and Control

Abstract

The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for linear operators, we can view the SRG as a generalization of the spectrum to multi-valued nonlinear operators. In this work, we further study the SRG of linear operators and characterize the SRG of block-diagonal and normal matrices.

Keywords

Cite

@article{arxiv.2001.02061,
  title  = {Scaled Relative Graph of Normal Matrices},
  author = {Xinmeng Huang and Ernest K. Ryu and Wotao Yin},
  journal= {arXiv preprint arXiv:2001.02061},
  year   = {2024}
}

Comments

Published in Journal of Convex Analysis

R2 v1 2026-06-23T13:04:59.859Z