Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations

Monnanda Erappa Shobha; Santhosh George

doi:10.1007/978-3-642-32112-2_35

Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations

Monnanda Erappa Shobha, Santhosh George

Department of Mathematics, Manipal Institute of Technology, Manipal

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.

Original language	English
Title of host publication	Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings
Pages	293-301
Number of pages	9
DOIs	https://doi.org/10.1007/978-3-642-32112-2_35
Publication status	Published - 2012
Event	International Conference on Eco-Friendly Computing and Communication Systems, ICECCS 2012 - Kochi, India Duration: 09-08-2012 → 11-08-2012

Publication series

Name	Communications in Computer and Information Science
Volume	305 CCIS
ISSN (Print)	1865-0929

Conference

Conference	International Conference on Eco-Friendly Computing and Communication Systems, ICECCS 2012
Country/Territory	India
City	Kochi
Period	09-08-12 → 11-08-12

All Science Journal Classification (ASJC) codes

Computer Science(all)
Mathematics(all)

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10.1007/978-3-642-32112-2_35

Cite this

Shobha, M. E., & George, S. (2012). Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations. In Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings (pp. 293-301). (Communications in Computer and Information Science; Vol. 305 CCIS). https://doi.org/10.1007/978-3-642-32112-2_35

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title = "Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations",

abstract = "Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.",

author = "Shobha, {Monnanda Erappa} and Santhosh George",

year = "2012",

doi = "10.1007/978-3-642-32112-2_35",

language = "English",

isbn = "9783642321115",

series = "Communications in Computer and Information Science",

pages = "293--301",

booktitle = "Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings",

note = "International Conference on Eco-Friendly Computing and Communication Systems, ICECCS 2012 ; Conference date: 09-08-2012 Through 11-08-2012",

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Shobha, ME & George, S 2012, Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations. in Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings. Communications in Computer and Information Science, vol. 305 CCIS, pp. 293-301, International Conference on Eco-Friendly Computing and Communication Systems, ICECCS 2012, Kochi, India, 09-08-12. https://doi.org/10.1007/978-3-642-32112-2_35

Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations. / Shobha, Monnanda Erappa; George, Santhosh.

Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings. 2012. p. 293-301 (Communications in Computer and Information Science; Vol. 305 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations

AU - Shobha, Monnanda Erappa

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N2 - Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.

AB - Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.

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BT - Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings

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Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations

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