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Scaled Relative Graph of Normal Matrices

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arxiv 2001.02061 v3 pith:NZYXWIZA submitted 2019-12-28 math.NA cs.NAmath.OC

Xinmeng Huang , Ernest K. Ryu , Wotao Yin This is my paper · ORCID
classification math.NAcs.NAmath.OC
keywords operatorsgraphlinearmatricesmulti-valuednonlinearnormalrelative
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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.

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Cited by 1 Pith paper

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  1. A Dissipativity Framework for Constructing Scaled Graphs

    math.OC 2025-07 conditional novelty 6.0 of 10

    A dissipativity-based LMI framework computes scaled graphs for LTI, reset, and piecewise-linear systems, with an exactness guarantee for normal LTI systems.

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