Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry |
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Authors: | Ryu Ernest K Hannah Robert Yin Wotao |
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Institution: | 1.Department of Mathematical Sciences, Seoul National University, Seoul, South Korea ;2.Department of Mathematics, University of California, Los Angeles, USA ; |
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Abstract: | 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.
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