Year: 2025
Type: preprint
Abstract: The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems from recent models in biology and phylogenetics, where problems of great practical significance are cast as optimization problems on (quasi-)metric spaces. We investigate a minimal algebraic setup that allows us to study a notion of differentiability suitable for Newton-type methods, called Newton differentiability. This notion of differentiability benefits from calculus rules and is sufficient to prove superlinear convergence of a Newton-type method. Finally, a Newton-Kantorovich-type theorem provides an inverse function result, applicable on (quasi-)metric spaces.
Source: arXiv (Cornell University)
Author: Pinta, Titus
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7101775183
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