Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations

Ioannis K. Argyros, Santhosh George, Shobha Monnanda Erappa

Research output: Contribution to journalArticle

Abstract

For the solution of nonlinear ill-posed problems, a Two Step Newton-Tikhonov methodology is proposed. Two implementations are discussed and applied to nonlinear ill-posed Hammerstein type operator equations KF(x) = y, where K defines the integral operator and F the function of the solution x on which K operates. In the first case, the Fre´ chet derivative of F is invertible in a neighbourhood which includes the initial guess x0 and the solution x^. In the second case, F is monotone. For both cases, local cubic convergence is established and order optimal error bounds are obtained by choosing the regularization parameter according to the the balancing principle of Pereverzev and Schock (2005).We also present the results of computational experiments giving the evidence of the reliability of our approach.

Original languageEnglish
Pages (from-to)303-323
Number of pages21
JournalRendiconti del Circolo Matematico di Palermo
Volume66
Issue number3
DOIs
Publication statusPublished - 01-12-2017
Externally publishedYes

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Cubic Convergence
Nonlinear Ill-posed Problems
Iterative Regularization
Convergence Order
Optimal Bound
Local Convergence
Regularization Parameter
Guess
Regularization Method
Operator Equation
Integral Operator
Computational Experiments
Balancing
Invertible
Error Bounds
Monotone
Iteration
Derivative
Methodology
Evidence

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Argyros, Ioannis K. ; George, Santhosh ; Monnanda Erappa, Shobha. / Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations. In: Rendiconti del Circolo Matematico di Palermo. 2017 ; Vol. 66, No. 3. pp. 303-323.
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Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations. / Argyros, Ioannis K.; George, Santhosh; Monnanda Erappa, Shobha.

In: Rendiconti del Circolo Matematico di Palermo, Vol. 66, No. 3, 01.12.2017, p. 303-323.

Research output: Contribution to journalArticle

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