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.
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