Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph. The SRG provides a correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of convergence.

中文翻译：

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缩放的相对图：通过二维欧几里得几何的非膨胀算子

应用数学中的许多迭代方法可以被认为是定点迭代，并且这些算法通常被分析分析，具有不等式。在本文中，我们提出了一种几何方法，使用一种称为缩放相对图的新工具来分析收缩和非膨胀不动点迭代。SRG 提供非线性算子和二维平面子集之间的对应关系。在这个框架下，二维平面中的几何参数成为收敛的严格证明。