How averaged is the projection? (2312.15421v1)

Published 24 Dec 2023 in math.FA, cs.NA, math.NA, and math.OC

Abstract: Projection operators are important in Analysis, Optimization and Algorithm. It is well known that these operators are firmly nonexpansive. In this paper, we provide an exact result that sharpens this well-known result. We develop the theory of averaged operators and provide a lower bound. We give a result on the avergedness of operator compositions. We also provide some nonlinear examples to illustrate our results.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Shuang Song

Collections

Sign up for free to add this paper to one or more collections.