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

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.

Copyright Heldermann Verlag 2026