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تسجيل مستخدم جديدScaled Relative Graph of Normal Matrices
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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 and normal matrices.
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Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure quaternion m
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Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an $mathcal{O}(1/k)$ rate with the constant determined by the averagedness coefficient, establishing small averagedness coefficient
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