Stochastic variance reduced gradient method for linear ill-posed inverse problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909141820243968 |
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| author | Jin, Qinian Chen, Liuhong |
| author_facet | Jin, Qinian Chen, Liuhong |
| contents | In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in Hilbert spaces. Under {\it a priori} choices of stopping indices, we derive a convergence rate result when the sought solution satisfies a benchmark source condition and establish a convergence result without using any source condition. To terminate the method in an {\it a posteriori} manner, we consider the discrepancy principle and show that it terminates the method in finite many iteration steps almost surely. Various numerical results are reported to test the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic variance reduced gradient method for linear ill-posed inverse problems Jin, Qinian Chen, Liuhong Numerical Analysis Optimization and Control In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in Hilbert spaces. Under {\it a priori} choices of stopping indices, we derive a convergence rate result when the sought solution satisfies a benchmark source condition and establish a convergence result without using any source condition. To terminate the method in an {\it a posteriori} manner, we consider the discrepancy principle and show that it terminates the method in finite many iteration steps almost surely. Various numerical results are reported to test the performance of the method. |
| title | Stochastic variance reduced gradient method for linear ill-posed inverse problems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2403.12460 |