{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T21:07:32Z","timestamp":1779311252374,"version":"3.51.4"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,5,25]],"date-time":"2013-05-25T00:00:00Z","timestamp":1369440000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2014,4]]},"DOI":"10.1007\/s11075-013-9719-6","type":"journal-article","created":{"date-parts":[[2013,5,24]],"date-time":"2013-05-24T09:02:51Z","timestamp":1369386171000},"page":"875-892","source":"Crossref","is-referenced-by-count":11,"title":["Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region"],"prefix":"10.1007","volume":"65","author":[{"given":"H. W.","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,5,25]]},"reference":[{"issue":"1","key":"9719_CR1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1515\/jiip.2001.9.1.13","volume":"9","author":"J Baumeister","year":"2001","unstructured":"Baumeister, J., Leit\u00e3o, A.: On iterative methods for solving ill-posed problems modeled by partial differential equations. J Inverse Ill-posed Prob 9(1), 13\u201330 (2001)","journal-title":"J Inverse Ill-posed Prob"},{"key":"9719_CR2","doi-asserted-by":"crossref","first-page":"095004","DOI":"10.1088\/0266-5611\/25\/9\/095004","volume":"25","author":"YJ Deng","year":"2009","unstructured":"Deng, Y.J., Liu, Z.H.: Iteration methods on sideways parabolic equations. Inverse Prob. 25, 095004 (2009)","journal-title":"Inverse Prob."},{"issue":"175","key":"9719_CR3","first-page":"135","volume":"47","author":"RS Falk","year":"1986","unstructured":"Falk, R.S., Monk, P.B.: Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson\u2019s equation. Math. Comp. 47(175), 135\u2013149 (1986)","journal-title":"Math. Comp."},{"issue":"2","key":"9719_CR4","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1080\/17415970701228246","volume":"16","author":"CL Fu","year":"2008","unstructured":"Fu, C.L., Li, H.F., Qian, Z., Xiong, X.T.: Fourier regularization method for solving a Cauchy problem for the Laplace equation. Inverse Prob. Sci. Eng. 16(2), 159\u2013169 (2008)","journal-title":"Inverse Prob. Sci. Eng."},{"key":"9719_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of inverse problems, volume 375 of mathematics and its applications","author":"HW Engl","year":"1996","unstructured":"Engl, H.W., Hanke, M., Neubauer, A.: Regularization of inverse problems, volume 375 of mathematics and its applications. Kluwer Academic Publishers Group, Dordrecht (1996)"},{"key":"9719_CR6","volume-title":"Lectures on Cauchy\u2019s problem in linear partial differential equations","author":"J Hadamard","year":"1953","unstructured":"Hadamard, J.: Lectures on Cauchy\u2019s problem in linear partial differential equations. Dover Publications, New York (1953)"},{"issue":"1","key":"9719_CR7","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1088\/0266-5611\/23\/1\/024","volume":"23","author":"DN H\u00e0o","year":"2007","unstructured":"H\u00e0o, D.N., Hien, P.M., Sahli, H.: Stability results for a Cauchy problem for an elliptic equation. Inverse Prob. 23(1), 421\u2013461 (2007)","journal-title":"Inverse Prob."},{"issue":"3\u20134","key":"9719_CR8","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/01630560008816965","volume":"21","author":"T Hohage","year":"2000","unstructured":"Hohage, T.: Regularization of exponentially ill-posed problems. Numer. Funct. Anal. Optim. 21(3\u20134), 439\u2013464 (2000)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9719_CR9","volume-title":"Inverse problems for partial differential equations, volume 127 of Applied Mathematical Sciences","author":"V Isakov","year":"2006","unstructured":"Isakov, V.: Inverse problems for partial differential equations, volume 127 of Applied Mathematical Sciences, 2nd edn. Springer, New York (2006)","edition":"2"},{"key":"9719_CR10","unstructured":"Jourhmane, M.: M\u00e9thode num\u00e9riques de r\u00e9solution d\u2019un probl\u00e8me d\u2019\u00e9lectro-enc\u00e9phalographie. PhD Thesis, University of Rennes I , France (1993)"},{"issue":"4","key":"9719_CR11","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1080\/10682760290004320","volume":"10","author":"M Jourhmane","year":"2002","unstructured":"Jourhmane, M., Mera, N.S.: An iterative algorithm for the backward heat conduction problem based on variable relaxation factors. Inverse Prob. Eng. 10(4), 293\u2013308 (2002)","journal-title":"Inverse Prob. Eng."},{"key":"9719_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5338-9","volume-title":"An introduction to the mathematical theory of inverse problems, volume 120 of Applied Mathematical Sciences","author":"A Kirsch","year":"1996","unstructured":"Kirsch, A.: An introduction to the mathematical theory of inverse problems, volume 120 of Applied Mathematical Sciences. Springer-Verlag, New York (1996)"},{"issue":"5","key":"9719_CR13","first-page":"144","volume":"1","author":"VA Kozlov","year":"1989","unstructured":"Kozlov, V.A., Maz\u2019ya, V.G.: On iterative procedures for solving ill-posed boundary value problems that preserve the differential equations (in Russian). Algebra i Analiz 1(5), 144\u2013170 (1989)","journal-title":"Algebra i Analiz"},{"issue":"1","key":"9719_CR14","first-page":"45","volume":"31","author":"VA Kozlov","year":"1991","unstructured":"Kozlov, V.A., Maz\u2019ya, V.G., Fomin, A.V.: An iterative method for solving the Cauchy problem for elliptic equations. Comput. Math. Phys. 31(1), 45\u201352 (1991)","journal-title":"Comput. Math. Phys."},{"key":"9719_CR15","unstructured":"Lavrentiev, M.M., Romanov, V.G., Shishatski, S.P.: Ill-posed problems of mathematical physics and analysis, volume 64 of Translations of Mathematical Monographs. American Mathematical Society, Providence (1986). Translated from the Russian by J. R, Schulenberger, Translation edited by Lev J. Leifman"},{"key":"9719_CR16","first-page":"35","volume":"23","author":"A Leit\u00e3o","year":"2002","unstructured":"Leit\u00e3o, A.: Mean value methods for solving the heat equation backwards in time. Matem\u00e1tica Contempora\u0302nea 23, 35\u201347 (2002)","journal-title":"Matem\u00e1tica Contempora\u0302nea"},{"key":"9719_CR17","doi-asserted-by":"crossref","unstructured":"Louis, A.K.: Inverse und schlecht gestellte Probleme. BG Teubner (1989)","DOI":"10.1007\/978-3-322-84808-6"},{"key":"9719_CR18","doi-asserted-by":"crossref","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., Nashed, Z., Aries, A.B.: Methods for solving incorrectly posed problems. Springer, New York (1984)"},{"key":"9719_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65711-5","volume-title":"Approximation of functions of several variables and imbedding theorems","author":"SM Nikol\u2019skii","year":"1975","unstructured":"Nikol\u2019skii, S.M.: Approximation of functions of several variables and imbedding theorems. Springer, Berlin (1975)"},{"issue":"2","key":"9719_CR20","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.amc.2008.05.009","volume":"203","author":"AL Qian","year":"2008","unstructured":"Qian, A.L.: A new wavelet method for solving an ill-posed problem. Appl. Math. Comput. 203(2), 635\u2013640 (2008)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"9719_CR21","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.jmaa.2007.05.040","volume":"338","author":"Z Qian","year":"2008","unstructured":"Qian, Z., Fu, C.L., Li, Z.P.: Two regularization methods for a Cauchy problem for the Laplace equation. J. Math. Anal. Appl. 338(1), 479\u2013489 (2008)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"9719_CR22","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1088\/0266-5611\/22\/3\/015","volume":"22","author":"T Regi\u0144ska","year":"2006","unstructured":"Regi\u0144ska, T., Regi\u0144ski, K.: Approximate solution of a Cauchy problem for the Helmholtz equation. Inverse Prob. 22(3), 975\u2013989 (2006)","journal-title":"Inverse Prob."},{"issue":"3","key":"9719_CR23","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1137\/S0036142997316955","volume":"36","author":"HJ Reinhardt","year":"1999","unstructured":"Reinhardt, H.J., Han, H., H\u00e0o, D.N.: Stability and regularization of a discrete approximation to the Cauchy problem for Laplace\u2019s equation. SIAM J. Numer. Anal. 36(3), 890\u2013905 (1999)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3\u20134","key":"9719_CR24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1080\/01630569808816834","volume":"19","author":"U Tautenhahn","year":"1998","unstructured":"Tautenhahn, U.: Optimality for ill-posed problems under general source conditions. Numer. Funct. Anal. Optim. 19(3\u20134), 377\u2013398 (1998)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9719_CR25","volume-title":"Solutions of ill-posed problems","author":"AN Tikhonov","year":"1977","unstructured":"Tikhonov, A.N., Arsenin, V.Y.: Solutions of ill-posed problems. V. H. Winston & Sons, Washington, D.C. (1977). Wiley, New York. Translated from the Russian, Preface by translation editor Fritz John, Scripta Series in Mathematics"},{"key":"9719_CR26","volume-title":"Iteration procedures in ill-posed problems (in Russian)","author":"GM Vainikko","year":"1986","unstructured":"Vainikko, G.M., Veretennikov, A.Y.: Iteration procedures in ill-posed problems (in Russian). Nau2 ka, Moscow (1986)"},{"issue":"2","key":"9719_CR27","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1137\/S0363012901389391","volume":"42","author":"T Wei","year":"2003","unstructured":"Wei, T., Hon, Y.C., Cheng, J.: Computation for multidimensional Cauchy problem. SIAM J. Control Optim. 42(2), 381\u2013396 (2003). (electronic)","journal-title":"SIAM J. Control Optim."},{"issue":"106","key":"9719_CR28","first-page":"1","volume":"2011","author":"HW Zhang","year":"2011","unstructured":"Zhang, H.W.: Modified quasi-boundary value method for Cauchy problems of elliptic equations with variable coefficients. Electron. J. Diff. Equat. 2011(106), 1\u201310 (2011)","journal-title":"Electron. J. Diff. Equat."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9719-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-013-9719-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9719-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T22:37:32Z","timestamp":1688251052000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-013-9719-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,25]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["9719"],"URL":"https:\/\/doi.org\/10.1007\/s11075-013-9719-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,25]]}}}