Weights in block iterative methods

نویسندگان

  • M. Abbasi Department of Mathematics, Iran University of Science and Technology, Tehran 16846-13114, Iran.
  • T. Nikazad Department of Mathematics, Iran University of Science and Technology, Tehran 16846-13114, Iran.
چکیده مقاله:

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibilityproblems, we give equivalency of our algorithms with sequential and simultaneous block Kaczmarzmethods explaining the optimal weights have been inherently used in Kaczmarz methods. In addi-tion, a convergence result is presented for simultaneous block Kaczmarz for the case of inconsistentlinear system of equations.

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عنوان ژورنال

دوره 5  شماره 2

صفحات  37- 49

تاریخ انتشار 2014-07-01

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