{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T03:33:10Z","timestamp":1771299190566,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T00:00:00Z","timestamp":1576800000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T00:00:00Z","timestamp":1576800000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"The work of Santhosh George is supported by the Core Research Grant by SERB, Department of Science and Technology, Govt. of India","award":["EMR\/2017\/001594"],"award-info":[{"award-number":["EMR\/2017\/001594"]}]},{"name":"National Board of Higher Mathematics (NBHM), Mumbai, India","award":["2\/40(56)\/2015\/R&D-II\/12987"],"award-info":[{"award-number":["2\/40(56)\/2015\/R&D-II\/12987"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s12190-019-01309-3","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T11:02:44Z","timestamp":1576839764000},"page":"87-105","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates"],"prefix":"10.1007","volume":"63","author":[{"given":"K.","family":"Kanagaraj","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. D.","family":"Reddy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santhosh","family":"George","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,12,20]]},"reference":[{"key":"1309_CR1","unstructured":"Arcangeli, R.: Pseudo-solution de l\u2019 equation $$Ax=y$$. C. R. Math. Acad. Sci. Paris Ser. A 263 A, 282\u2013285 (1966)"},{"key":"1309_CR2","first-page":"581","volume":"15","author":"D Bianchi","year":"2015","unstructured":"Bianchi, D., Buccini, A., Donatelli, M., Serra-Capizzano, S.: Iterated fractional Tikhonov regularization. PAMM 15, 581\u2013582 (2015)","journal-title":"Iterated fractional Tikhonov regularization. PAMM"},{"key":"1309_CR3","first-page":"73","volume":"47","author":"D Bianchi","year":"2017","unstructured":"Bianchi, D., Donatelli, M.: On generalized iterated Tikhonov regularization with operator dependent seminorms. Electron. Trans. Numer. Anal. 47, 73\u201399 (2017)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"5","key":"1309_CR4","doi-asserted-by":"publisher","first-page":"055005","DOI":"10.1088\/0266-5611\/31\/5\/055005","volume":"31","author":"D Bianchi","year":"2015","unstructured":"Bianchi, D., Buccini, A., Donatelli, M., Serra-Capizzano, S.: Iterated fractional Tikhonov regularization. Inverse Probl. 31(5), 055005 (2015)","journal-title":"Inverse Probl."},{"key":"1309_CR5","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF00941281","volume":"52","author":"HW Engl","year":"1987","unstructured":"Engl, H.W.: Discrepancy principle for Tikhonov regularization of Ill-posed problems leading to optimal convergence rates. J. Optim. Theory Appl. 52, 209\u2013215 (1987)","journal-title":"J. Optim. Theory Appl."},{"key":"1309_CR6","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0021-9045(87)90113-4","volume":"49","author":"HW Engl","year":"1987","unstructured":"Engl, H.W.: On the choice of regularization parameter for iterated Tikhonov regularization of Ill-posed problems. J. Approx. Theory. 49, 55\u201363 (1987)","journal-title":"J. Approx. Theory."},{"key":"1309_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of Inverse Problems","author":"HW Engl","year":"1996","unstructured":"Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer, Dordrecht (1996)"},{"key":"1309_CR8","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/978-3-0348-9317-6_10","volume-title":"Constructive Methods for the Practical Treatment of Integral Equations","author":"HW Engl","year":"1985","unstructured":"Engl, H.W., Neubauer, A.: Optimal discrepancy principle for the Tikhonov regularization of integral equations of the first kind. In: Hammerlin, G., Hoffmann, K.H. (eds.) Constructive Methods for the Practical Treatment of Integral Equations, pp. 120\u2013141. Birkh\u00e4user, Basel (1985)"},{"key":"1309_CR9","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/B978-0-12-239040-1.50011-9","volume-title":"Inverse and Ill-Posed Problems","author":"HW Engl","year":"1987","unstructured":"Engl, H.W., Neubauer, A.: Optimal parameter choice for ordinary and iterated tikhonov regularization. In: Engl, H.W., Groetsch, C.W. (eds.) Inverse and Ill-Posed Problems, pp. 97\u2013125. Academic Press, New York (1987)"},{"key":"1309_CR10","first-page":"405","volume":"45","author":"HW Engl","year":"1985","unstructured":"Engl, H.W., Neubauer, A.: An improved version of Marti\u2019s method for solving ill-posed linear integral equations. Math. Comput. 45, 405\u2013416 (1985)","journal-title":"Math. Comput."},{"key":"1309_CR11","unstructured":"George, S.: Approximation method for ill-posed operator equations, Ph. D Thesis, Goa University (1994)"},{"issue":"7&8","key":"1309_CR12","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1080\/01630569808816858","volume":"19","author":"S George","year":"1998","unstructured":"George, S., Nair, M.T.: On a generalized arcangelis method for Tikhonov regularization with inexact data. Numer. Funct. Anal. Optim. 19(7&8), 773\u2013787 (1998)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"1","key":"1309_CR13","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/BF02191771","volume":"83","author":"S George","year":"1994","unstructured":"George, S., Nair, M.T.: Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates. J. Optim. Theory Appl. 83(1), 217\u2013222 (1994)","journal-title":"J. Optim. Theory Appl."},{"issue":"6","key":"1309_CR14","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1515\/jiip-2014-0050","volume":"23","author":"D Gerth","year":"2015","unstructured":"Gerth, D., Klann, E., Ramalau, R., Reichel, L.: On fractional Tikhonov regularization. J. Inverse Ill Posed Probl. 23(6), 611\u2013625 (2015)","journal-title":"J. Inverse Ill Posed Probl."},{"key":"1309_CR15","volume-title":"Generalized Inverse of Linear Operators","author":"CW Groetsch","year":"1977","unstructured":"Groetsch, C.W.: Generalized Inverse of Linear Operators. Representation and Application. Marcel Dekker, New York (1977)"},{"key":"1309_CR16","volume-title":"The Theory of Tikhonov Regularization Method for Fredholm Equations of the First Kind","author":"CW Groetsch","year":"1984","unstructured":"Groetsch, C.W.: The Theory of Tikhonov Regularization Method for Fredholm Equations of the First Kind. Pitman, Boston (1984)"},{"key":"1309_CR17","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/978-3-0348-5460-3_7","volume-title":"Improperly Posed Problems and Their Numerical Treatments","author":"CW Groetsch","year":"1983","unstructured":"Groetsch, C.W.: Comments on Morozov\u2019s Discrepancy Principle. In: Hammerlin, G., Hoffmann, K.H. (eds.) Improperly Posed Problems and Their Numerical Treatments, pp. 97\u2013104. Birkh\u00e4user, Basel (1983)"},{"issue":"3","key":"1309_CR18","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1080\/00036818408839519","volume":"18","author":"CW Groetsch","year":"1984","unstructured":"Groetsch, C.W., Schock, E.: Asymptotic convergence rate of Arcangeli\u2019s method for Ill-posed problems. Appl. Anal. 18(3), 175\u2013182 (1984)","journal-title":"Appl. Anal."},{"issue":"4","key":"1309_CR19","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1007\/BF01199309","volume":"11","author":"JE Guacaneme","year":"1988","unstructured":"Guacaneme, J.E.: An optimal parameter choice for regularized Ill-posed problems. Integr. Equ. Oper. Theory. 11(4), 610\u2013613 (1988)","journal-title":"Integr. Equ. Oper. Theory."},{"key":"1309_CR20","doi-asserted-by":"crossref","unstructured":"Hansen, P.C.: Regularization tools version 4.0 for Matlab 7.3. Numer. Algorithms. 46(2), 189\u2013194 (2007)","DOI":"10.1007\/s11075-007-9136-9"},{"issue":"1","key":"1309_CR21","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s10543-011-0313-9","volume":"51","author":"ME Hochstenbach","year":"2011","unstructured":"Hochstenbach, M.E., Reichel, L.: Fractional Tikhonov regularization for linear discrete Ill-posed problems. BIT Numer. Math. 51(1), 197\u2013215 (2011)","journal-title":"BIT Numer. Math."},{"key":"1309_CR22","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s10665-013-9671-4","volume":"93","author":"ME Hochstenbach","year":"2015","unstructured":"Hochstenbach, M.E., Noschese, S., Reichel, L.: Fractional regularization matrices for linear discrete Ill-posed problems. J. Eng. Math. 93, 113\u2013129 (2015)","journal-title":"J. Eng. Math."},{"issue":"2","key":"1309_CR23","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s11075-012-9575-9","volume":"60","author":"TK Huckle","year":"2015","unstructured":"Huckle, T.K., Sedlacek, M.: Tikhonov-Phillips regularization with operator dependent seminorms. Numer. Algorithms 60(2), 339\u2013353 (2015)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"1309_CR24","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1088\/0266-5611\/24\/2\/025018","volume":"24","author":"E Klann","year":"2008","unstructured":"Klann, E., Ramalau, R.: Regularization by fractional filter methods and data smoothing. Inverse Probl. 24(2), 113\u2013129 (2008)","journal-title":"Inverse Probl."},{"key":"1309_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-84808-6","volume-title":"Inverse und Schlecht Gestellte Probleme","author":"AK Louis","year":"1989","unstructured":"Louis, A.K.: Inverse und Schlecht Gestellte Probleme. Teubner, Stuttgart (1989)"},{"key":"1309_CR26","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.cam.2017.04.017","volume":"324","author":"S Morigi","year":"2017","unstructured":"Morigi, S., Reichel, L., Sgallari, F.: Fractional Tikhonov regularization with a nonlinear penalty term. J. Comput. Appl. Math. 324, 142\u2013154 (2017)","journal-title":"J. Comput. Appl. Math."},{"key":"1309_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5280-1","volume-title":"Methods for Solving Incorrectly Posed Problems","author":"VA Morozov","year":"1984","unstructured":"Morozov, V.A.: Methods for Solving Incorrectly Posed Problems. Springer, New York (1984)"},{"key":"1309_CR28","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0041-5553(68)90034-7","volume":"8","author":"VA Morozov","year":"1996","unstructured":"Morozov, V.A.: The error principle in the solution of operational equations by the regularization method. USSR Comput. Math. Math. Phys. 8, 63\u201367 (1996)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"1309_CR29","doi-asserted-by":"publisher","DOI":"10.1142\/7055","volume-title":"Linear Operator Equations","author":"MT Nair","year":"2009","unstructured":"Nair, M.T.: Linear Operator Equations. Approximation and Regularization. World Scientific, Singapore (2009)"},{"key":"1309_CR30","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1007\/BF01203127","volume":"15","author":"MT Nair","year":"1992","unstructured":"Nair, M.T.: A generalization of Arcangeli\u2019s method for Ill-posed problems leading to optimal rates. Integr. Equ. Oper. Theory 15, 1042\u20131046 (1992)","journal-title":"Integr. Equ. Oper. Theory"},{"issue":"2","key":"1309_CR31","doi-asserted-by":"publisher","first-page":"2039","DOI":"10.1007\/s40314-017-0433-1","volume":"37","author":"GD Reddy","year":"2018","unstructured":"Reddy, G.D.: The parameter choice rules for weighted Tikhonov regularization scheme. Comput. Appl. Math. 37(2), 2039\u20132052 (2018)","journal-title":"Comput. Appl. Math."},{"issue":"6","key":"1309_CR32","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1007\/BF01195873","volume":"7","author":"E Schock","year":"1984","unstructured":"Schock, E.: Parameter choice by discrepancy principles for the approximate solution of Ill-posed problems. Integr. Equ. Oper. Theory 7(6), 895\u2013898 (1984)","journal-title":"Integr. Equ. Oper. Theory"},{"issue":"1","key":"1309_CR33","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF00934896","volume":"44","author":"E Schock","year":"1984","unstructured":"Schock, E.: On the asymptotic order of accuracy of Tikhonov regularization. J. Optim. Theory Appl. 44(1), 95\u2013104 (1984)","journal-title":"J. Optim. Theory Appl."},{"key":"1309_CR34","volume-title":"Solutions of Ill-Posed Problems","author":"AN Tikhonov","year":"1977","unstructured":"Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Wiley, New York (1977)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01309-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-019-01309-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01309-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,19]],"date-time":"2020-12-19T00:38:19Z","timestamp":1608338299000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-019-01309-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,20]]},"references-count":34,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["1309"],"URL":"https:\/\/doi.org\/10.1007\/s12190-019-01309-3","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,20]]},"assertion":[{"value":"6 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}