Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems

Duan-Peng Ling; Wenlong Zhang

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arXiv · 2605.18259

Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems

Duan-Peng Ling·Wenlong Zhang

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Abstract

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.

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BibTeX RIS

Duan-Peng Ling, Wenlong Zhang. 2026-05-18. Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems. https://arxiv.org/abs/2605.18259

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