Finite dimensional realization of a Tikhonov gradient type-method under weak conditions

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• 作者：Vorkady S. Shubha ; Santhosh George…
• 关键词：Iterative method ; Nonlinear ill ; posed equations ; Tikhonov regularization ; Adaptive method
• 刊名：Rendiconti del Circolo Matematico di Palermo
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：65
• 期：3
• 页码：395-410
• 全文大小：1,239 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Geometry
  Analysis
  Applications of Mathematics
  
• 出版者：Springer Milan
• ISSN：1973-4409
• 卷排序：65

文摘

In this paper we consider projection techniques to obtain the finite dimensional realization of a Tikhonov gradient type-method considered in George et al. (Local convergence of a Tikhonov gradient type-method under weak conditions, communicated, 2016) for approximating a solution \(\hat{x}\) of the nonlinear ill-posed operator equation \(F(x)=y\). The main advantage of the proposed method is that the inverse of the operator F is not involved in the method. The regularization parameter is chosen according to the adaptive method considered by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005). We also derive optimal stopping conditions on the number of iterations necessary for obtaining the optimal order of convergence. Using two numerical examples we compare our results with an existing method to justify the theoretical results.