Stochastic variance reduced gradient method for linear ill-posed inverse problems
<|reference_start|>Stochastic variance reduced gradient method for linear ill-posed inverse problems: 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.<|reference_end|>
@article{jin2024stochastic,
    title={Stochastic variance reduced gradient method for linear ill-posed inverse
  problems},
    author={Qinian Jin and Liuhong Chen},
    journal={arXiv preprint arXiv:2403.12460},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12460},
    primaryClass={math.NA cs.NA math.OC}
}