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The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and $N$ inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.
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참고문헌 (38)
참고문헌 신청
Y. Alber / 2006 / Nonlinear Ill-Posed Problems of Monotone Type / Springer
P. K. Anh / 2014 / Parallel methods for regularizing systems of equations involving accretive operators / Appl. Anal. 93(10):2136~2157
P. K. Anh / 2009 / Parallel iterative regularization methods for solving systems of ill-posed equations / Appl. Math. Comput. 212(2):542~550
P. K. Anh / 2010 / Parallel iterative regularization algorithms for large overdetermined linear systems / Int. J. Comput. Methods 7(4):525~537
I. K. Argyros / 2014 / Expanding the applicability of Lavrentiev regularization methods for ill-posed equations under general source condition / Nonl. Funct. Anal. Appl. 19(2):177~192
P. K. Anh / 2014 / Parallel methods for regularizing systems of equations involving accretive operators / Appl. Anal. 93(10):2136~2157
P. K. Anh / 2009 / Parallel iterative regularization methods for solving systems of ill-posed equations / Appl. Math. Comput. 212(2):542~550
P. K. Anh / 2010 / Parallel iterative regularization algorithms for large overdetermined linear systems / Int. J. Comput. Methods 7(4):525~537
I. K. Argyros / 2014 / Expanding the applicability of Lavrentiev regularization methods for ill-posed equations under general source condition / Nonl. Funct. Anal. Appl. 19(2):177~192
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