A randomized progressive iterative regularization method for data fitting problems

TL;DR

This paper introduces a randomized iterative regularization method for data fitting with noise, effective for large-scale problems, and includes an optimal parameter estimation approach validated by numerical experiments.

Contribution

It proposes a novel randomized progressive iterative regularization technique with an optimal parameter estimation strategy for data fitting problems.

Findings

Converges in expectation to the least-squares solution.

Effective for large-scale matrix computations.

Validated by numerical results in curve and surface fitting.

Abstract

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares solution. Furthermore, we present an optimal estimation for the regularization parameter, which inspires the construction of self-consistent algorithms without prior information. The numerical results confirm the theoretical analysis and show the performance in curve and surface fittings.