scholarly journals Cyclic Coordinate-Update Algorithms for Fixed-Point Problems: Analysis and Applications

2017 ◽  
Vol 39 (4) ◽  
pp. A1280-A1300 ◽  
Author(s):  
Yat Tin Chow ◽  
Tianyu Wu ◽  
Wotao Yin
Keyword(s):  
Fixed Point ◽  
Fixed Point Problems ◽  
Coordinate Update

A cyclic coordinate-update fixed point algorithm

2019 ◽  
Vol 35 (3) ◽  
pp. 365-370
Author(s):  
BO PENG ◽  
◽  
HONG-KUN XU ◽  
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Cartesian Product ◽  
Fixed Point Problems ◽  
Fixed Point Algorithm ◽  
Block Spaces ◽  
Coordinate Update

We prove that a cyclic coordinate fixed point algorithm for nonexpansive mappings when the underlying Hilbert space is decomposed into a Cartesian product of finitely many block spaces is weakly convergent to a fixed point of the mapping under investigation. Our result relaxes a condition imposed on the stepsizes of Theorem 3.4 of Chow, et al [Chow, Y. T., Wu, T. and Yin, W., Cyclic coordinate-update algorithms for fixed-point problems: analysis and applcations, SIAM J. Sci. Comput., 39 (2017), No. 4, A1280–A1300].

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