Journal of Convex Analysis 33 (2026), No. 1&2, 145--154
Copyright Heldermann Verlag 2026
Scaled Relative Graphs of Normal Matrices
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
Wotao Yin
Dept. of Mathematics, University of California, Los Angeles, U.S.A.
wotaoyin@math.ucla.edu
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.
Keywords: Scaled relative graph, non-Euclidean geometry, hyperbolic geometry, normal matrix.
MSC: 47H05, 47H09, 51M04, 52A55, 90C25.
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