Finite-sample analysis of rotation operator under $l_2$ norm and $l_\infty$ norm

TL;DR

This paper analyzes the convergence and finite-sample bounds of a 2D rotation operator under $l_2$ and $l_ abla$ norms, including stochastic noise effects, supported by simulations and future extension discussions.

Contribution

It provides the first finite-sample analysis of the rotation operator under different norms with stochastic noise considerations.

Findings

Finite-sample bounds established for the rotation operator.

Convergence properties under $l_2$ and $l_ abla$ norms analyzed.

Simulations validate theoretical results.

Abstract

In this article, we consider a special operator called the two-dimensional rotation operator and analyze its convergence and finite-sample bounds under the $l_2$ norm and $l_\infty$ norm with constant step size. We then consider the same problem with stochastic noise with affine variance. Furthermore, simulations are provided to illustrate our results. Finally, we conclude this article by proposing some possible future extensions.