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Paper   IPM / M / 15381
School of Mathematics
  Title:   Perturbed fixed point iterative methods based on pattern structure
  Author(s):  Touraj Nikazad (Joint with M. Abbasi)
  Status:   Published
  Journal: Math. Methods Appl. Sci.
  Vol.:  41
  Year:  2018
  Pages:   5582-5592
  Supported by:  IPM
We introduce a new idea of algorithmic structure, called assigning algorithm, using a finite collection of a subclass of strictly quasi-nonexpansive operators. This new algorithm allows the iteration vectors to take steps on a pattern which is based on a connected directed acyclic graph. The sequential, simultaneous, and string-averaging methods for solving convex feasibility problems are the special cases of the new algorithm which may be used to reduce idle time of processors in parallel implementations.We give a convergence analysis for such algorithmic structure with perturbation. Also, we extend some existence results of the split common fixed point problem based on the new algorithm. The performance of the new algorithm is illustrated with numerical examples from computed tomography.

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