Parallel methods for regularizing systems of equations involving accretive operators

Abstract

In this paper, two parallel methods for solving systems of accretive operator equations in Banach spaces are studied. The convergence analysis of the methods in both free-noise and noisy data cases is provided.

Keywords:

• uniformly smooth and uniformly convex Banach spaces
• accretive and inverse uniformly accretive operators
• iterative regularization method
• Newton-type method
• parallel computation

AMS Subject Classifications:

• 47J06
• 47J25
• 65J15
• 65J20
• 65Y05

Acknowledgments

The authors would like to thank the referees for their careful reading and comments which improved the presentation of the paper. The first author of this manuscript wishes to express his gratitude to Vietnam Institute for Advanced Study in Mathematics for financial support.