Corpus ID: 210023761

Scaled Relative Graph of Normal Matrices

@article{Huang2020ScaledRG,
  title={Scaled Relative Graph of Normal Matrices},
  author={X. Huang and E. K. Ryu and Wotao Yin},
  journal={ArXiv},
  year={2020},
  volume={abs/2001.02061}
}
  • X. Huang, E. K. Ryu, Wotao Yin
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • The Scaled Relative Graph (SRG) by Ryu, Hannah, and Yin (arXiv:1902.09788, 2019) 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… CONTINUE READING

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    References

    SHOWING 1-10 OF 11 REFERENCES
    Tight Coefficients of Averaged Operators via Scaled Relative Graph
    • 2
    • PDF
    Scaled Relative Graph: Nonexpansive operators via 2D Euclidean Geometry.
    • 7
    • PDF
    On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • 2,256
    • PDF
    On compositions of special cases of Lipschitz continuous operators
    • 3
    • PDF
    Tight Global Linear Convergence Rate Bounds for Operator Splitting Methods
    • 14
    • PDF
    Splitting methods for monotone operators with applications to parallel optimization
    • 273
    Ueber die sogenannte Nicht-Euklidische Geometrie
    • 153
    • PDF
    Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
    • 137
    • PDF
    Lunds universitet
    • lecture notes: Large-scale convex optimization
    • 2015