Seminário de Otimização & Problemas Inversos – 17/04/2023 às 14 horas
Seminário de Otimização & Problemas Inversos
On stochastic projective type methods for solving large scale systems of ill-posed equations
Antonio Leitão (UFSC)
Resumo: 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). 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.
Data: Segunda-feira, 17 de abril de 2023 às 14 horas.
Local: Auditório Airton Silva, MTM-CFM
Maiores informações: http://mtm.ufsc.br/~maicon/seminar