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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.18259 |
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| _version_ | 1866909054139367424 |
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| author | Ling, Duan-Peng Zhang, Wenlong |
| author_facet | Ling, Duan-Peng Zhang, Wenlong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems Ling, Duan-Peng Zhang, Wenlong Numerical Analysis 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. |
| title | Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.18259 |