Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution

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• 作者：M. Yu. Kokurin
• 关键词：operator equations ; irregular operator ; Hilbert space ; normally solvable operator ; Gauss–Newton methods ; iterative regularization ; termination criterion ; estimate of accuracy
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：56
• 期：9
• 页码：1523-1535
• 全文大小：323 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662
• 卷排序：56

文摘

A group of iteratively regularized methods of Gauss–Newton type for solving irregular nonlinear equations with smooth operators in a Hilbert space under the condition of normal solvability of the derivative of the operator at the solution is considered. A priori and a posteriori methods for termination of iterations are studied, and estimates of the accuracy of approximations obtained are found. It is shown that, in the case of a priori termination, the accuracy of the approximation is proportional to the error in the input data. Under certain additional conditions, the same estimate is established for a posterior termination from the residual principle. These results generalize known similar estimates for linear equations with a normally solvable operator.