On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations

Author:

Rabelo J C,Saporito Y F,Leitão AORCID

Abstract

Abstract In this article we investigate a family of stochastic gradient type methods for solving systems of linear ill-posed equations. The method under consideration is a stochastic version of the projective Landweber–Kaczmarz method in Leitão and Svaiter (2016 Inverse Problems 32 025004) (see also Leitão and Svaiter (2018 Numer. Funct. Anal. Optim. 39 1153–80)). In the case of exact data, mean square convergence to zero of the iteration error is proven. In the noisy data case, we couple our method with an a priori stopping rule and characterize it as a regularization method for solving systems of linear ill-posed operator equations. Numerical tests are presented for two linear ill-posed problems: (i) a Hilbert matrix type system with over 108 equations; (ii) a big data linear regression problem with real data. The obtained results indicate superior performance of the proposed method when compared with other well-established random iterations. Our preliminary investigation indicates that the proposed iteration is a promising alternative for computing stable approximate solutions of large scale systems of linear ill-posed equations.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Publisher

IOP Publishing

Subject

Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science

Reference43 articles.

1. On Levenberg–Marquardt–Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations;Baumeister;Inverse Problem Imaging,2010

2. Legendre functions and the method of random Bregman projections;Bauschke;J. Convex Anal.,1997

3. Construction of fixed points of nonlinear mappings in Hilbert space;Browder;J. Math. Anal. Appl.,1967

4. Regularizing Newton–Kaczmarz methods for nonlinear ill-posed problems;Burger;SIAM J. Numer. Anal.,2006

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