Scaled Relative Graph of Normal Matrices

Xinmeng Huang, Ernest K. Ryu, and Wotao Yin



The Scaled Relative Graph (SRG) by Ryu, Hannah, and Yin 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.



X. Huang, E. Ryu, and W. Yin, Scaled relative graph of normal matrices, arXiv:2001.02061, 2020.

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