A Stochastic Iteratively Regularized Gauss-Newton Method

Autor:	Bergou, El Houcine, Chada, Neil K., Diouane, Youssef
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Mathematics - Optimization and Control 65N21 65C35 65K10 93E24
Druh dokumentu:	Working Paper
Popis:	This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for infinite-dimensional problems. Recent work have extended this method to handle sequential observations, rather than a single instance of the data, demonstrating notable improvements in reconstruction accuracy. In this paper, we further extend these methods to a stochastic framework through mini-batching, introducing a new algorithm, the stochastic iteratively regularized Gauss-Newton method (SIRGNM). Our algorithm is designed through the use randomized sketching. We provide an analysis for the SIRGNM, which includes a preliminary error decomposition and a convergence analysis, related to the residuals. We provide numerical experiments on a 2D elliptic PDE example. This illustrates the effectiveness of the SIRGNM, through maintaining a similar level of accuracy while reducing on the computational time. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.12381 Zobrazit plný text záznamu View this record from Arxiv