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Hari
Shanker Gupta. (2012) A numerical study of variable coefficient elliptic Cauchy problem via projection method. International Journal of Computer Mathematics 89:6, pages 795-809.
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Mejdi Azaïez, Faker Ben Belgacem, Duc Thang Du & Faten Jelassi. (2011) A finite element model for the data completion problem: analysis and assessment. Inverse Problems in Science and Engineering 19:8, pages 1063-1086.
Read now
Read now
Johan Helsing & B. Tomas Johansson. (2011) Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations. Inverse Problems in Science and Engineering 19:5, pages 717-727.
Read now
Read now
Yonghong Yao & Yeal Je Cho. (2010) A strong convergence of a modified Krasnoselskii‐Mann method for non‐expansive mappings in Hilbert spaces. Mathematical Modelling and Analysis 15:2, pages 265-274.
Read now
Read now
Johan Helsing & B. Tomas Johansson. (2010) Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques. Inverse Problems in Science and Engineering 18:3, pages 381-399.
Read now
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Roman Chapko & B. Tomas Johansson. (2009) An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant. Inverse Problems in Science and Engineering 17:7, pages 871-883.
Read now
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Ricardo Celorrio & Andreas Hofinger. (2008) A real-time solution for an inverse Cauchy problem in cardiology. Inverse Problems in Science and Engineering 16:3, pages 281-301.
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T.S. Jang & S.L. Han. (2008) Application of Tikhonov's regularization to unstable water waves of the two-dimensional fluid flow: spectrum with compact support. Ships and Offshore Structures 3:1, pages 41-47.
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Articles from other publishers (39)
N. E. Sibiryakov, D. Yu. Kochkin, O. A. Kabov & A. L. Karchevsky. (2023) Determining the Heat Flux Density in the Area of a Contact Line during the Evaporation of Liquid into a Bubble. Journal of Applied and Industrial Mathematics 17:3, pages 628-639.
Crossref
Crossref
Mikhail A. Botchev, Sergey I. Kabanikhin, Maxim A. Shishlenin & Eugene E. Tyrtyshnikov. (2023) The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method. Journal of Inverse and Ill-posed Problems 0:0.
Crossref
Crossref
Rahul Shukla, Rajendra Pant & Winter Sinkala. (2022) A General Picard-Mann Iterative Method for Approximating Fixed Points of Nonexpansive Mappings with Applications. Symmetry 14:8, pages 1741.
Crossref
Crossref
Hamid Ouaissa, Abdelkrim Chakib, Abdeljalil Nachaoui & Mourad Nachaoui. (2022) On Numerical Approaches for Solving an Inverse Cauchy Stokes Problem. Applied Mathematics & Optimization 85:1.
Crossref
Crossref
Nikolay Koshev, Nikolay Yavich, Mikhail Malovichko, Ekaterina Skidchenko & Maxim Fedorov. (2020) FEM-based Scalp-to-Cortex EEG data mapping via the solution of the Cauchy problem. Journal of Inverse and Ill-posed Problems 28:4, pages 517-532.
Crossref
Crossref
Rahul Shukla & Rajendra Pant. (2019) Robustness of Theta Method for Nonexpansive Mappings. Iranian Journal of Science and Technology, Transactions A: Science 43:5, pages 2275-2284.
Crossref
Crossref
George Baravdish, Ihor Borachok, Roman Chapko, B. Tomas Johansson & Marián Slodička. (2018) An iterative method for the Cauchy problem for second-order elliptic equations. International Journal of Mechanical Sciences 142-143, pages 216-223.
Crossref
Crossref
Nguyen Huy Tuan, Le Duc Thang & Daniel Lesnic. (2016) A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source. Journal of Mathematical Analysis and Applications 434:2, pages 1376-1393.
Crossref
Crossref
Lili Chang, Wei Gong, Guiquan Sun & Ningning Yan. (2015) PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems and Imaging 9:3, pages 791-814.
Crossref
Crossref
Bing Yan & Si-Xun Huang. (2014) Variational regularization method of solving the Cauchy problem for Laplace's equation: Innovation of the Grad—Shafranov (GS) reconstruction. Chinese Physics B 23:10, pages 109402.
Crossref
Crossref
H. J. LiX. S. FengJ. XiangP. B. Zuo. (2013) New approach for solving the inverse boundary value problem of Laplace's equation on a circle: Technique renovation of the Grad-Shafranov (GS) reconstruction. Journal of Geophysical Research: Space Physics 118:6, pages 2876-2881.
Crossref
Crossref
Thouraya N. Baranger, B. Tomas Johansson & Romain Rischette. 2013. Applied Inverse Problems. Applied Inverse Problems
183
197
.
Isao Yamada, Masahiro Yukawa & Masao Yamagishi. 2011. Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Fixed-Point Algorithms for Inverse Problems in Science and Engineering
345
390
.
A Leitão & M Marques Alves. (2010) Multiple level-sets for elliptic Cauchy problems in three dimensional domains. Journal of Physics: Conference Series 255, pages 012005.
Crossref
Crossref
A El-Badia & M Farah. (2010) A stable recovering of dipole sources from partial boundary measurements. Inverse Problems 26:11, pages 115006.
Crossref
Crossref
Shuang Wang & Changsong Hu. (2010) Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces. Fixed Point Theory and Applications 2010:1.
Crossref
Crossref
A.M. Saddeek. (2010) Coincidence points by generalized Mann iterates with applications in Hilbert spaces. Nonlinear Analysis: Theory, Methods & Applications 72:5, pages 2262-2270.
Crossref
Crossref
LC Ceng, YC Liou & JC Yao. (2010) Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces. Fixed Point Theory and Applications 2010:1.
Crossref
Crossref
H Egger & A Leitão. (2009) Nonlinear regularization methods for ill-posed problems with piecewise constant or strongly varying solutions. Inverse Problems 25:11, pages 115014.
Crossref
Crossref
Yonghong Yao, Yeong Cheng Liou & Giuseppe Marino. (2009) Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces. Fixed Point Theory and Applications 2009:1.
Crossref
Crossref
Hui Cao, Michael V Klibanov & Sergei V Pereverzev. (2009) A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation. Inverse Problems 25:3, pages 035005.
Crossref
Crossref
E. Sincich. (2009) Stability and reconstruction for inverse corrosion problems. Journal of Inverse and Ill-posed Problems 17:8.
Crossref
Crossref
Hui Cao, Sergei V Pereverzev & Eva Sincich. (2008) Natural linearization for corrosion identification. Journal of Physics: Conference Series 135, pages 012027.
Crossref
Crossref
S Anzengruber, F Bauer, A Leitão & R Ramlau. (2008) New algorithms for parallel MRI. Journal of Physics: Conference Series 135, pages 012009.
Crossref
Crossref
F Ben Belgacem & S-M Kaber. (2008) Quadratic optimization in ill-posed problems. Inverse Problems 24:5, pages 055002.
Crossref
Crossref
Yonghong Yao, Haiyun Zhou & Yeong-Cheng Liou. (2008) Iterative algorithms with variable anchors for non-expansive mappings. Journal of Applied Mathematics and Computing 28:1-2, pages 39-49.
Crossref
Crossref
Roman Chapko & B. Tomas Johansson. (2008) An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions. Inverse Problems & Imaging 2:3, pages 317-333.
Crossref
Crossref
Yeong-Cheng Liou & Yonghong Yao. (2008) Iterative Algorithms for Nonexpansive Mappings. Fixed Point Theory and Applications 2008, pages 1-11.
Crossref
Crossref
Tomoya Takeuchi & Masahiro Yamamoto. (2008) Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation. SIAM Journal on Scientific Computing 31:1, pages 112-142.
Crossref
Crossref
A Leitão & M Marques Alves. (2007) On level set type methods for elliptic Cauchy problems. Inverse Problems 23:5, pages 2207-2222.
Crossref
Crossref
Hui Cao & Sergei V Pereverzev. (2007) The balancing principle for the regularization of elliptic Cauchy problems. Inverse Problems 23:5, pages 1943-1961.
Crossref
Crossref
Tae-Hwa Kim & Hong-Kun Xu. (2007) Robustness of Mann's algorithm for nonexpansive mappings. Journal of Mathematical Analysis and Applications 327:2, pages 1105-1115.
Crossref
Crossref
Giovanni Alessandrini & Eva Sincich. (2007) Solving elliptic Cauchy problems and the identification of nonlinear corrosion. Journal of Computational and Applied Mathematics 198:2, pages 307-320.
Crossref
Crossref
Mejdi Azaïez, Faker Ben Belgacem & Henda El Fekih. (2006) On Cauchy's problem: II. Completion, regularization and approximation. Inverse Problems 22:4, pages 1307-1336.
Crossref
Crossref
T. Johansson. (2006) An iterative method for reconstruction of temperature. Journal of Inverse and Ill-posed Problems 14:3, pages 267-278.
Crossref
Crossref
Faker Ben Belgacem & Henda El Fekih. (2005) On Cauchy's problem: I. A variational Steklov–Poincaré theory. Inverse Problems 21:6, pages 1915-1936.
Crossref
Crossref
Heinz W. Engl & Philipp Kügler. 2005. Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems. Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems
3
47
.
Ulrich Kohlenbach. (2003) Uniform asymptotic regularity for Mann iterates. Journal of Mathematical Analysis and Applications 279:2, pages 531-544.
Crossref
Crossref
Patrick L. Combettes & Teemu Pennanen. (2002) Generalized Mann iterates for constructing fixed points in Hilbert spaces. Journal of Mathematical Analysis and Applications 275:2, pages 521-536.
Crossref
Crossref