Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems
数值分析
2026-05-19 v1 数值分析
摘要
We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic error bounds for two noise models: expectation bounds for independent zero-mean bounded-variance noise, and high-probability bounds for independent sub-Gaussian noise. The analysis yields an a priori parameter-choice rule and suggests an adaptive strategy suitable for large-scale computation. Numerical experiments support the theory and show that the predicted parameter is nearly optimal and that the adaptive method is effective in practice.
引用
@article{arxiv.2605.18259,
title = {Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems},
author = {Duan-Peng Ling and Wenlong Zhang},
journal= {arXiv preprint arXiv:2605.18259},
year = {2026}
}