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## Plato, Robert

Compute Distance To:
 Author ID: plato.robert Published as: Plato, Robert; Plato, R. External Links: MGP · dblp · GND
 Documents Indexed: 35 Publications since 1989, including 6 Books Reviewing Activity: 114 Reviews
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#### Co-Authors

 24 single-authored 4 Hofmann, Bernd 4 Vainikko, Gennadi 1 Eicke, Bertolt 1 Grigorieff, Rolf Dieter 1 Hämarik, Uno 1 Louis, Alfred Karl 1 Mathé, Peter
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#### Serials

 3 Numerical Functional Analysis and Optimization 3 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Computational Methods in Applied Mathematics 1 Matimyás Matematika 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 BIT 1 Calcolo 1 Journal of Optimization Theory and Applications 1 Journal of Integral Equations and Applications 1 Numerical Algorithms 1 Linear Algebra and its Applications 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Graduate Studies in Mathematics
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#### Fields

 34 Numerical analysis (65-XX) 18 Operator theory (47-XX) 14 Integral equations (45-XX) 5 Approximations and expansions (41-XX) 2 Partial differential equations (35-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX)

#### Citations contained in zbMATH Open

27 Publications have been cited 200 times in 163 Documents Cited by Year
On the regularization of projection methods for solving ill-posed problems. Zbl 0675.65053
Plato, R.; Vainikko, G.
1990
Optimal algorithms for solving linear ill-posed problems yield regularization methods. Zbl 0691.65040
Plato, Robert
1990
On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations. Zbl 0864.65034
Plato, Robert
1996
The Galerkin scheme for Lavrentiev’s $$m$$-times iterated method to solve linear accretive Volterra integral equations of the first kind. Zbl 0882.65135
Plato, Robert
1997
The instability of some gradient methods for ill-posed problems. Zbl 0714.65056
Eicke, Bertolt; Louis, Alfred K.; Plato, Robert
1990
The regularizing properties of the composite trapezoidal method for weakly singular Volterra integral equations of the first kind. Zbl 1245.65187
Plato, Robert
2012
Resolvent estimates for Abel integral operators and the regularization of associated first kind integral equations. Zbl 0904.65136
Plato, R.
1997
On ill-posedness concepts, stable solvability and saturation. Zbl 06864435
Hofmann, Bernd; Plato, Robert
2018
On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces. Zbl 0865.65039
Plato, R.; Hämarik, U.
1996
Concise numerical mathematics. Translated from the German by Richard Le Borne and Sabine Le Borne. Zbl 1022.65002
Plato, Robert
2003
Fractional multistep methods for weakly singular Volterra integral equations of the first kind with perturbed data. Zbl 1079.65137
Plato, Robert
2005
Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096
Plato, Robert; Mathé, Peter; Hofmann, Bernd
2018
On a minimax equality for seminorms. Zbl 0829.46005
Grigorieff, R. D.; Plato, R.
1995
Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems. Zbl 1366.65058
Plato, Robert
2017
The method of conjugate residuals for solving the Galerkin equations associated with symmetric positive semidefinite ill-posed problems. Zbl 0916.65057
Plato, R.
1998
Lavrentiev’s method for linear Volterra integral equations of the first kind, with applications to the non-destructive testing of optical-fibre preforms. Zbl 0880.65121
Plato, Robert
1997
On the regularization of the Ritz-Galerkin method for solving ill-posed problems. Zbl 0711.65041
Plato, Robert; Vainikko, Gennadi
1989
The conjugate gradient method for linear ill-posed problems with operator perturbations. Zbl 0935.65059
Plato, Robert
1999
On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves. Zbl 1008.65098
Plato, R.; Vainikko, G.
2001
Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term. Zbl 07192776
Hofmann, Bernd; Plato, Robert
2020
Numerical mathematics compact. (Numerische Mathematik kompakt. Grundlagenwissen für Studium und Praxis.) Zbl 0963.65001
Plato, Robert
2000
The solution of linear semidefinite ill-posed problems by the conjugate residual method. Zbl 0961.65049
Plato, R.
2000
The Lavrentiev-regularized Galerkin method for linear accretive ill-posed problems. Zbl 0935.65058
Plato, Robert
1998
Fast solution of periodic integral equations by GMRES. Zbl 1026.65127
Plato, R.; Vainikko, G.
2001
Workbook for numerical mathematics. Problems, solutions and applications. (Übungsbuch zur numerischen Mathematik. Aufgaben, Lösungen und Anwendungen.) Zbl 1067.65002
Plato, Robert
2004
The regularizing properties of multistep methods for first kind Volterra integral equations with smooth kernels. Zbl 1355.65183
Plato, Robert
2017
Über die Diskretisierung und Regularisierung schlecht gestellter Probleme. (Discretization and regularization of ill-posed problems). Zbl 0696.65054
Plato, Robert
1990
Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term. Zbl 07192776
Hofmann, Bernd; Plato, Robert
2020
On ill-posedness concepts, stable solvability and saturation. Zbl 06864435
Hofmann, Bernd; Plato, Robert
2018
Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096
Plato, Robert; Mathé, Peter; Hofmann, Bernd
2018
Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems. Zbl 1366.65058
Plato, Robert
2017
The regularizing properties of multistep methods for first kind Volterra integral equations with smooth kernels. Zbl 1355.65183
Plato, Robert
2017
The regularizing properties of the composite trapezoidal method for weakly singular Volterra integral equations of the first kind. Zbl 1245.65187
Plato, Robert
2012
Fractional multistep methods for weakly singular Volterra integral equations of the first kind with perturbed data. Zbl 1079.65137
Plato, Robert
2005
Workbook for numerical mathematics. Problems, solutions and applications. (Übungsbuch zur numerischen Mathematik. Aufgaben, Lösungen und Anwendungen.) Zbl 1067.65002
Plato, Robert
2004
Concise numerical mathematics. Translated from the German by Richard Le Borne and Sabine Le Borne. Zbl 1022.65002
Plato, Robert
2003
On the fast and fully discretized solution of integral and pseudo-differential equations on smooth curves. Zbl 1008.65098
Plato, R.; Vainikko, G.
2001
Fast solution of periodic integral equations by GMRES. Zbl 1026.65127
Plato, R.; Vainikko, G.
2001
Numerical mathematics compact. (Numerische Mathematik kompakt. Grundlagenwissen für Studium und Praxis.) Zbl 0963.65001
Plato, Robert
2000
The solution of linear semidefinite ill-posed problems by the conjugate residual method. Zbl 0961.65049
Plato, R.
2000
The conjugate gradient method for linear ill-posed problems with operator perturbations. Zbl 0935.65059
Plato, Robert
1999
The method of conjugate residuals for solving the Galerkin equations associated with symmetric positive semidefinite ill-posed problems. Zbl 0916.65057
Plato, R.
1998
The Lavrentiev-regularized Galerkin method for linear accretive ill-posed problems. Zbl 0935.65058
Plato, Robert
1998
The Galerkin scheme for Lavrentiev’s $$m$$-times iterated method to solve linear accretive Volterra integral equations of the first kind. Zbl 0882.65135
Plato, Robert
1997
Resolvent estimates for Abel integral operators and the regularization of associated first kind integral equations. Zbl 0904.65136
Plato, R.
1997
Lavrentiev’s method for linear Volterra integral equations of the first kind, with applications to the non-destructive testing of optical-fibre preforms. Zbl 0880.65121
Plato, Robert
1997
On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations. Zbl 0864.65034
Plato, Robert
1996
On pseudo-optimal parameter choices and stopping rules for regularization methods in Banach spaces. Zbl 0865.65039
Plato, R.; Hämarik, U.
1996
On a minimax equality for seminorms. Zbl 0829.46005
Grigorieff, R. D.; Plato, R.
1995
On the regularization of projection methods for solving ill-posed problems. Zbl 0675.65053
Plato, R.; Vainikko, G.
1990
Optimal algorithms for solving linear ill-posed problems yield regularization methods. Zbl 0691.65040
Plato, Robert
1990
The instability of some gradient methods for ill-posed problems. Zbl 0714.65056
Eicke, Bertolt; Louis, Alfred K.; Plato, Robert
1990
Über die Diskretisierung und Regularisierung schlecht gestellter Probleme. (Discretization and regularization of ill-posed problems). Zbl 0696.65054
Plato, Robert
1990
On the regularization of the Ritz-Galerkin method for solving ill-posed problems. Zbl 0711.65041
Plato, Robert; Vainikko, Gennadi
1989
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#### Cited by 198 Authors

 14 Hofmann, Bernd 14 Plato, Robert 11 Pereverzev, Sergei V. 7 Kaltenbacher, Barbara 7 Mathé, Peter 7 Solodky, Sergei G. 7 Tautenhahn, Ulrich 6 Yang, Hongqi 5 Luo, Xingjun 5 Schock, Eberhard 4 Chen, Zhongying 4 Nair, M. Thamban 4 Zeng, Chunmei 3 Favati, Paola 3 George, Santhosh 3 Janno, Jaan 3 Li, Fanchun 3 Lotti, Grazia 3 Louis, Alfred Karl 3 Menchi, Ornella 3 Myleiko, Ganna L. 3 Romani, Francesco 3 Semenova, Evgeniya V. 2 Abdel-Aziz, Mohammedi R. 2 Bica, Alexandru Mihai 2 Chen, Dehan 2 Cheng, Sirui 2 Ding, Shengpei 2 Eicke, Bertolt 2 Estatico, Claudio 2 Freeden, Willi 2 Hämarik, Uno 2 Hanke-Bourgeois, Martin 2 Hofmann, Christopher 2 Hohage, Thorsten 2 Jia, Zhongxiao 2 Jin, Qinian 2 Johansson, B. Tomas 2 Krishnan, Venkateswaran P. 2 Lebedeva, Evgeniya V. 2 Lesnic, Daniel 2 Lu, Shuai 2 Maass, Peter 2 Miranker, Willard Lee 2 Nashed, M. Zuhair 2 Nedaiasl, Khadijeh 2 Neubauer, Andreas 2 Rajan, M. P. 2 Ramlau, Ronny 2 Reichel, Lothar 2 Roy, Souvik 2 Schröter, Torsten 2 Schuster, Thomas 2 Solodky, Sergey G. 2 Tkachenko, Pavlo 2 Vainikko, Gennadi 2 Volynets, Evgeny A. 2 Yang, Suhua 2 Yousept, Irwin 2 Zuckerman, Gregg J. 1 Abdeljawad, Thabet 1 Abramovitz, B. 1 Ahn, Soyoung 1 Al-Musallam, Fadhel A. 1 Alqudah, Manar A. 1 Amato, Umberto 1 Ambartsoumian, Gaik 1 Antoniadis, Anestis 1 Argyros, Ioannis Konstantinos 1 Arridge, Simon R. 1 Azaïez, Mejdi 1 Bebiano, Natália Isabel Quadros 1 Ben Belgacem, Faker 1 Blanchard, Gilles 1 Bonesky, Thomas 1 Burger, Martin 1 Caponnetto, Andrea 1 Cegielski, Andrzej 1 Chandrashekar, Praveen 1 Choi, U Jin 1 Curila, Mircea 1 Curila, Sorin 1 da Providência Santarém e Costa, João 1 Dai, Hua 1 Das Roy, Samprita 1 De Vito, Ernesto 1 Dehbozorgi, Raziyeh 1 Deng, Liangjian 1 Dihlmann, Markus A. 1 Đinh Nho Hào 1 Du, Duc Thang 1 Du, Lingling 1 Du, Nailin 1 Du, Shukai 1 Egger, Herbert 1 El-Alem, Mahmoud M. 1 Erb, Wolfgang 1 Gerth, Daniel 1 Gong, Maoguo 1 Gorenflo, Rudolf ...and 98 more Authors
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#### Cited in 56 Serials

 17 Numerical Functional Analysis and Optimization 13 Journal of Inverse and Ill-Posed Problems 8 Inverse Problems 8 Journal of Computational and Applied Mathematics 8 Journal of Integral Equations and Applications 6 Applied Mathematics and Computation 5 Applicable Analysis 5 Journal of Mathematical Analysis and Applications 5 Journal of Complexity 4 Ukrainian Mathematical Journal 4 Numerische Mathematik 4 Inverse Problems and Imaging 3 Computers & Mathematics with Applications 3 Mathematics of Computation 3 BIT 3 Journal of Optimization Theory and Applications 3 Zeitschrift für Analysis und ihre Anwendungen 3 Numerical Algorithms 3 International Journal of Computer Mathematics 3 Abstract and Applied Analysis 3 Computational Methods in Applied Mathematics 3 Inverse Problems in Science and Engineering 2 Applied Numerical Mathematics 2 Journal of Mathematical Sciences (New York) 2 ETNA. Electronic Transactions on Numerical Analysis 2 Advances in Computational Mathematics 2 Journal of Applied Logic 2 Analysis and Applications (Singapore) 2 GEM - International Journal on Geomathematics 1 Linear and Multilinear Algebra 1 Computing 1 Integral Equations and Operator Theory 1 Journal of Multivariate Analysis 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Acta Applicandae Mathematicae 1 Optimization 1 SIAM Journal on Matrix Analysis and Applications 1 European Journal of Applied Mathematics 1 Games and Economic Behavior 1 Historia Mathematica 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Imaging and Vision 1 Russian Mathematics 1 Computational Optimization and Applications 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Mathematical Problems in Engineering 1 Doklady Mathematics 1 Methodology and Computing in Applied Probability 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics and Computing 1 Acta Numerica 1 SIAM Journal on Imaging Sciences 1 Frontiers of Computer Science
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#### Cited in 28 Fields

 140 Numerical analysis (65-XX) 69 Operator theory (47-XX) 43 Integral equations (45-XX) 27 Partial differential equations (35-XX) 8 Information and communication theory, circuits (94-XX) 6 Biology and other natural sciences (92-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Statistics (62-XX) 4 Fluid mechanics (76-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Ordinary differential equations (34-XX) 3 Integral transforms, operational calculus (44-XX) 3 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 3 Computer science (68-XX) 3 Geophysics (86-XX) 2 Mathematical logic and foundations (03-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)