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.

翻译：缩放相对图（SRG）是一种几何工具，它将多值非线性算子的作用映射到二维平面上，用于分析各类迭代方法的收敛性。由于SRG包含了线性算子的谱，我们可以将SRG视为谱向多值非线性算子的推广。在本工作中，我们进一步研究了线性算子的SRG，并刻画了块对角矩阵与正规矩阵的SRG。