Convergence rate results for steepest descent type method for nonlinear ill-posed equations

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• 作者：Santhosh George ; ^{nitksanthosh@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{sgeorge@nitk.ac.in" class="auth_mail" title="E-mail the corresponding author} ; M. Sabari ^{msabarijothi16@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear ill-posed problem ; Steepest descent method ; Minimal error method ; Regularization method ; Discrepancy principle
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：294
• 期：Complete
• 页码：169-179
• 全文大小：383 K

文摘

Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper.