A randomized progressive iterative regularization method for data fitting problems

2025/06/04 by Cen, Dakang, Zhang, Wenlong, Zhong, Junbin · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.03526

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.

Citations

• Distributed Tikhonov regularization for ill-posed inverse problems from a Bayesian perspective
• On a progressive and iterative approximation method with memory for least square fitting
• On a progressive and iterative approximation method with memory for least square fitting
• Progressive and iterative approximation for least squares B-spline curve and surface fitting

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• An efficient iteration method to reconstruct the drift term from the final measurement

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