Edit Profile (opens in new tab) Gockenbach, Mark S. Co-Author Distance Author ID: gockenbach.mark-s Published as: Gockenbach, Mark S.; Gockenbach, M. S.; Gockenbach, Mark more...less Documents Indexed: 33 Publications since 1995, including 5 Books Co-Authors: 19 Co-Authors with 25 Joint Publications 690 Co-Co-Authors all top 5 Co-Authors 7 single-authored 8 Khan, Akhtar Ali 8 Symes, William W. 4 Jadamba, Baasansuren 2 Al-Jamal, Mohammad F. 2 Kearsley, Anthony José 2 Roberts, Matthew Jake 2 Winkler, Brian C. 1 Alomari, Abedel-Karrem 1 Cox, Steven J. 1 Crane, Daniel K. 1 Crossen, E. 1 Gorgin, Elaheh 1 Liu, Chang 1 Petro, Matthew J. 1 Reynolds, Daniel R. 1 Schmidtke, Kristin 1 Shen, Peng 1 Tammer, Christiane 1 Tapia, Richard A. all top 5 Serials 4 Mathematics and Mechanics of Solids 3 Inverse Problems 3 SIAM Journal on Numerical Analysis 2 Computers & Mathematics with Applications 2 ACM Transactions on Mathematical Software 2 Inverse Problems in Science and Engineering 1 Optimization 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 Optimization and Engineering 1 Journal of Industrial and Management Optimization 1 International Journal of Mathematics and Computer Science 1 The Carus Mathematical Monographs 1 Involve 1 Discrete Mathematics and its Applications all top 5 Fields 20 Numerical analysis (65-XX) 15 Partial differential equations (35-XX) 7 Mechanics of deformable solids (74-XX) 5 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Operations research, mathematical programming (90-XX) 3 Computer science (68-XX) 3 Biology and other natural sciences (92-XX) 2 Ordinary differential equations (34-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 25 Publications have been cited 247 times in 148 Documents Cited by ▼ Year ▼ Understanding and implementing the finite element method. Zbl 1105.65112 Gockenbach, Mark S. 54 2006 An abstract framework for elliptic inverse problems. I: An output least-squares approach. Zbl 1153.74021 Gockenbach, Mark S.; Khan, Akhtar A. 48 2007 An abstract framework for elliptic inverse problems. II: An augmented Lagrangian approach. Zbl 1197.74048 Gockenbach, Mark S.; Khan, Akhtar A. 24 2009 An equation error approach for the elasticity imaging inverse problem for predicting tumor location. Zbl 1352.92087 Crossen, E.; Gockenbach, M. S.; Jadamba, B.; Khan, A. A.; Winkler, B. 18 2014 Identification of Lamé parameters in linear elasticity: a fixed point approach. Zbl 1085.35127 Gockenbach, Mark S.; Khan, Akhtar A. 18 2005 Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters. Zbl 1258.74087 Gockenbach, M. S.; Jadamba, B.; Khan, A. A. 16 2008 Numerical estimation of discontinuous coefficients by the method of equation error. Zbl 1111.35110 Gockenbach, M. S.; Jadamba, B.; Khan, A. A. 11 2006 Stability and error estimates for an equation error method for elliptic equations. Zbl 1250.35179 Al-Jamal, Mohammad F.; Gockenbach, Mark S. 9 2012 Linear inverse problems and Tikhonov regularization. Zbl 1367.65085 Gockenbach, Mark S. 7 2016 Recovering planar Lamé moduli from a single-traction experiment. Zbl 1001.74512 Cox, Steven J.; Gockenbach, Mark 6 1997 A variational method for recovering planar Lamé moduli. Zbl 1024.74007 Chen, Jun; Gockenbach, Mark S. 5 2002 Proximal methods for the elastography inverse problem of tumor identification using an equation error approach. Zbl 1319.35297 Gockenbach, Mark S.; Jadamba, Baasansuren; Khan, Akhtar A.; Tammer, Christiane; Winkler, Brian 5 2015 Partial differential equations. Analytical and numerical methods. 2nd ed. Zbl 1410.65002 Gockenbach, Mark S. 5 2011 Optimal signal sets for non-Gaussian detectors. Zbl 1032.90531 Gockenbach, Mark S.; Kearsley, Anthony J. 3 1999 Partial differential equations. Analytical and numerical methods. With a foreword by William Symes. Zbl 1022.35001 Gockenbach, Mark S. 3 2002 The output least-squares approach to estimating Lamé moduli. Zbl 1126.35096 Gockenbach, Mark S. 3 2007 Finite-dimensional linear algebra. Zbl 1202.15002 Gockenbach, Mark S. 3 2010 Efficient and automatic implementation of the adjoint state method. Zbl 1070.65560 Gockenbach, Mark S.; Reynolds, Daniel R.; Shen, Peng; Symes, William W. 2 2002 Smoothing via elliptic operators with application to edge detection. Zbl 07039137 Al-Jamal, Mohammad F.; Alomari, A. K.; Gockenbach, Mark S. 1 2018 On the convergence of a heuristic parameter choice rule for Tikhonov regularization. Zbl 1398.65118 Gockenbach, Mark S.; Gorgin, Elaheh 1 2018 Approximating the generalized singular value expansion. Zbl 1397.65084 Gockenbach, Mark S.; Roberts, Matthew J. 1 2018 An infeasible point method for minimizing the Lennard-Jones potential. Zbl 0898.90121 Gockenbach, Mark S.; Kearsley, Anthony J.; Symes, William W. 1 1997 Generalizing the GSVD. Zbl 1347.65100 Gockenbach, Mark S. 1 2016 A convex objective functional for elliptic inverse problems. Zbl 1158.35103 Gockenbach, M. S.; Khan, A. A. 1 2006 Newton’s law of heating and the heat equation. Zbl 1185.35117 Gockenbach, Mark; Schmidtke, Kristin 1 2009 Smoothing via elliptic operators with application to edge detection. Zbl 07039137 Al-Jamal, Mohammad F.; Alomari, A. K.; Gockenbach, Mark S. 1 2018 On the convergence of a heuristic parameter choice rule for Tikhonov regularization. Zbl 1398.65118 Gockenbach, Mark S.; Gorgin, Elaheh 1 2018 Approximating the generalized singular value expansion. Zbl 1397.65084 Gockenbach, Mark S.; Roberts, Matthew J. 1 2018 Linear inverse problems and Tikhonov regularization. Zbl 1367.65085 Gockenbach, Mark S. 7 2016 Generalizing the GSVD. Zbl 1347.65100 Gockenbach, Mark S. 1 2016 Proximal methods for the elastography inverse problem of tumor identification using an equation error approach. Zbl 1319.35297 Gockenbach, Mark S.; Jadamba, Baasansuren; Khan, Akhtar A.; Tammer, Christiane; Winkler, Brian 5 2015 An equation error approach for the elasticity imaging inverse problem for predicting tumor location. Zbl 1352.92087 Crossen, E.; Gockenbach, M. S.; Jadamba, B.; Khan, A. A.; Winkler, B. 18 2014 Stability and error estimates for an equation error method for elliptic equations. Zbl 1250.35179 Al-Jamal, Mohammad F.; Gockenbach, Mark S. 9 2012 Partial differential equations. Analytical and numerical methods. 2nd ed. Zbl 1410.65002 Gockenbach, Mark S. 5 2011 Finite-dimensional linear algebra. Zbl 1202.15002 Gockenbach, Mark S. 3 2010 An abstract framework for elliptic inverse problems. II: An augmented Lagrangian approach. Zbl 1197.74048 Gockenbach, Mark S.; Khan, Akhtar A. 24 2009 Newton’s law of heating and the heat equation. Zbl 1185.35117 Gockenbach, Mark; Schmidtke, Kristin 1 2009 Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters. Zbl 1258.74087 Gockenbach, M. S.; Jadamba, B.; Khan, A. A. 16 2008 An abstract framework for elliptic inverse problems. I: An output least-squares approach. Zbl 1153.74021 Gockenbach, Mark S.; Khan, Akhtar A. 48 2007 The output least-squares approach to estimating Lamé moduli. Zbl 1126.35096 Gockenbach, Mark S. 3 2007 Understanding and implementing the finite element method. Zbl 1105.65112 Gockenbach, Mark S. 54 2006 Numerical estimation of discontinuous coefficients by the method of equation error. Zbl 1111.35110 Gockenbach, M. S.; Jadamba, B.; Khan, A. A. 11 2006 A convex objective functional for elliptic inverse problems. Zbl 1158.35103 Gockenbach, M. S.; Khan, A. A. 1 2006 Identification of Lamé parameters in linear elasticity: a fixed point approach. Zbl 1085.35127 Gockenbach, Mark S.; Khan, Akhtar A. 18 2005 A variational method for recovering planar Lamé moduli. Zbl 1024.74007 Chen, Jun; Gockenbach, Mark S. 5 2002 Partial differential equations. Analytical and numerical methods. With a foreword by William Symes. Zbl 1022.35001 Gockenbach, Mark S. 3 2002 Efficient and automatic implementation of the adjoint state method. Zbl 1070.65560 Gockenbach, Mark S.; Reynolds, Daniel R.; Shen, Peng; Symes, William W. 2 2002 Optimal signal sets for non-Gaussian detectors. Zbl 1032.90531 Gockenbach, Mark S.; Kearsley, Anthony J. 3 1999 Recovering planar Lamé moduli from a single-traction experiment. Zbl 1001.74512 Cox, Steven J.; Gockenbach, Mark 6 1997 An infeasible point method for minimizing the Lennard-Jones potential. Zbl 0898.90121 Gockenbach, Mark S.; Kearsley, Anthony J.; Symes, William W. 1 1997 all cited Publications top 5 cited Publications all top 5 Cited by 278 Authors 31 Khan, Akhtar Ali 21 Jadamba, Baasansuren 18 Sama, Miguel 10 Gockenbach, Mark S. 9 Tammer, Christiane 7 Winkler, Brian C. 5 Raciti, Fabio 4 Gwinner, Joachim 4 Oberai, Assad A. 4 Quyen, Tran Nhan Tam 4 Vadillo, Fernando 3 Liu, Tao 3 Migórski, Stanisław 3 Petra, Noemi 3 Richards, Michael 3 Zeng, Biao 2 Aquino, Wilkins 2 Barbone, Paul E. 2 Basaran, Osman A. 2 Blaheta, Radim 2 Bonnet, Marc 2 Bucataru, Mihai 2 de la Hoz, Francisco 2 Đinh Nho Hào 2 Doubova, Anna 2 Fang, Liang 2 Garg, Vishrut 2 Habibi, Noora 2 Haslinger, Jaroslav 2 Hinze, Michael 2 Jannesari, Zahra 2 Kähler, Ralf 2 Liu, Jie 2 Liu, Songshu 2 Marin, Liviu 2 Mesforush, Ali 2 Meyers, Johan 2 Petra, Cosmin G. 2 Roberts, Matthew Jake 2 Rodrigo, Carmen 2 Starkloff, Hans-Jörg 2 Tatari, Mehdi 2 Vandewalle, Stefan G. 2 Vatulyan, Aleksandr Ovanesovich 2 Yang, Yidan 2 Zhao, Jingjun 1 Abbasbandy, Saeid 1 Abdelhamid, Talaat 1 Aceves-Sánchez, Pedro 1 Al-Jamal, Mohammad F. 1 Alam, Muhammad Mahbub 1 Albocher, Uri 1 Ali, Baharin 1 Alomari, Abedel-Karrem 1 Ambati, Marreddy 1 Antoni, Jérôme 1 Appadu, A. R. 1 Appelö, Daniel 1 Aransay, Jesús 1 Aubry, Denis 1 Awasthi, Chaitanya 1 Aymard, Benjamin 1 Babaniyi, Olalekan A. 1 Baiz, Othmane 1 Banerjee, Biswanath 1 Bangura, Raymond Manna 1 Baniabedalruhman, Ahmad 1 Bauer, Daniel J. 1 Benaissa, Hicham 1 Bernardi, Mara S. 1 Birkeland, Rolf G. 1 Bourguignon, Sébastien 1 Boutaayamou, Idriss 1 Brunk, Aaron 1 Bukshtynov, Vladislav 1 Cahill, Nathan D. 1 Calvetti, Daniela 1 Carey, Michelle 1 Casteilla, Louis 1 Caya, P. 1 Cengizci, Aslıhan Dursun 1 Cengizci, Süleyman 1 Červený, Jakub 1 Chen, Fuchen 1 Chen, Rongliang 1 Cheng, Xiaoliang 1 Chō, Muneo 1 Choi, Youngsoo 1 Chung, Tsz Shun Eric 1 Cîmpean, Iulian 1 Clason, Christian 1 Contu, Pietro 1 Crane, Daniel K. 1 Crossen, E. 1 Dambrine, Marc 1 Darve, Eric 1 Das Roy, Samprita 1 de Lorenzis, Laura 1 Degond, Pierre 1 Denina, O. V. ...and 178 more Authors all top 5 Cited in 63 Serials 10 Inverse Problems 9 Journal of Computational and Applied Mathematics 6 Computers & Mathematics with Applications 6 Journal of Computational Physics 6 Applied Mathematics and Computation 6 Optimization 6 Inverse Problems in Science and Engineering 5 Computer Methods in Applied Mechanics and Engineering 5 SIAM Journal on Numerical Analysis 4 Journal of Inverse and Ill-Posed Problems 4 Journal of Nonlinear and Variational Analysis 3 International Journal for Numerical Methods in Engineering 3 Journal of Scientific Computing 3 SIAM Journal on Applied Mathematics 3 Mathematics and Mechanics of Solids 3 Computational Methods in Applied Mathematics 2 Journal of Fluid Mechanics 2 Numerical Functional Analysis and Optimization 2 Computational Mechanics 2 Numerical Algorithms 2 Applied Mathematical Modelling 2 Journal of Convex Analysis 2 Optimization Methods & Software 2 Discrete and Continuous Dynamical Systems. Series B 2 Optimization Letters 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Optimization 1 Journal of Multivariate Analysis 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Numerical Methods for Partial Differential Equations 1 Annals of Operations Research 1 Japan Journal of Industrial and Applied Mathematics 1 Journal of Global Optimization 1 European Journal of Operational Research 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 SIAM Journal on Scientific Computing 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Journal of Functional Programming 1 Engineering Analysis with Boundary Elements 1 Mathematical Problems in Engineering 1 Finance and Stochastics 1 Journal of Applied Mechanics and Technical Physics 1 Communications in Nonlinear Science and Numerical Simulation 1 Nonlinear Analysis. Real World Applications 1 Archives of Computational Methods in Engineering 1 Mathematical Biosciences and Engineering 1 Boundary Value Problems 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Networks and Heterogeneous Media 1 Inverse Problems and Imaging 1 SIAM Journal on Imaging Sciences 1 Numerical Mathematics: Theory, Methods and Applications 1 Advances in Applied Mathematics and Mechanics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Journal of Mathematical Modeling 1 Computational Methods for Differential Equations 1 Open Mathematics all top 5 Cited in 26 Fields 84 Numerical analysis (65-XX) 63 Partial differential equations (35-XX) 38 Mechanics of deformable solids (74-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 19 Operations research, mathematical programming (90-XX) 16 Biology and other natural sciences (92-XX) 12 Fluid mechanics (76-XX) 10 Operator theory (47-XX) 5 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Functional analysis (46-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year