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.

Author information

Contact details are reproduced from the original publication and may be historical.

Xinmeng Huang

Dept. Applied Math. & Comp. Science, University of Pennsylvania, Philadelphia, U.S.A.

xinmengh@sas.upenn.edu

Ernest K. Ryu

Dept. of Mathematics, University of California, Los Angeles, U.S.A.

eryu@math.ucla.edu

Keywords

  • Scaled relative graph
  • non-Euclidean geometry
  • hyperbolic geometry
  • normal matrix

Mathematics Subject Classification

47H05, 47H09, 51M04, 52A55, 90C25

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Suggested citation

X. Huang, E. K. Ryu, W. Yin. “Scaled Relative Graphs of Normal Matrices.” Journal of Convex Analysis 33 (2026), No. 1&2, 145–154. https://doi.org/10.68381/jca33009

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.