Year: 2026
Type: preprint
Abstract: The paper extends the Scaled Relative Graph (SRG) framework of Ryu, Hannah, and Yin from Hilbert spaces to normed spaces. Our extension replaces the inner product with a regular pairing, whose asymmetry gives rise to directional angles and, in turn, directional SRGs. Directional SRGs are shown to provide geometric containment tests certifying key operator properties, including contraction and monotonicity. Calculus rules for SRGs under scaling, inversion, addition, and composition are also derived. The theory is illustrated by numerical examples, including a graphical analysis of the contractivity of Bellman operators using directional SRGs.
Source: arXiv (Cornell University)
Author: Padoan, Alberto
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7150812114
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