Publikationsliste Plato
Publications Dr. Robert Plato, Department of Mathematics, Siegen University
Textbooks
- Basiswissen Numerik
- 1. Auflage, Springer, 2023. 269 S. ISBN 978-3-662-66569-5
- Numerische Mathematik kompakt -- Grundlagenwissen für
Studium und Praxis
- 5. Auflage, Springer, 2021. 449 S. ISBN 978-3-662-64109-5
- Übungsbuch zur numerischen Mathematik
- 2. Auflage, Verlag Vieweg+Teubner, 2010. viii+216 S. ISBN 978-3-8348-1212-4
- Concise Numerical Mathematics
- American Mathematical Society, 2003. 460 S., 2003
Preprints
- A note on a predictor--corrector method for ordinary fractional differential equations
Scientific Papers
- Variational regularization with oversmoothing penalty in Banach spaces
- In Inverse Problems, Regularization Methods and Related Topics -- A Volume in Honour of Thamban Nair, S. V. Pereverzyev, R. Radha and S.~Sampath (Eds.), Springer New York, to appear
- with B. Hofmann
- arXiv Preprint No. 2206.02010
- New results for variational regularization with oversmoothing penalty term in Banach spaces
- Comm. Anal. Comp. 1(2):94--115, 2023
- with B. Hofmann and C. Klinkhammer
- arXiv Preprint No. 2305.00232
- Analysis of the discrepancy principle for Tikhonov regularization under low order source conditions
- Inverse Problems 39(10): 105014, 2023
- with C. Klinkhammer
- arXiv Preprint No. 2212.13366
- Convergence results and low order rates for nonlinear
Tikhonov regularization with oversmoothing penalty term
- ETNA 53:313--328, 2020
- with B. Hofmann
- arXiv Preprint No. 1911.00669
- A regularized variational inequality approach for
nonlinear monotone ill-posed equations
- JOTA 182(2):525--539, 2019
- with B. Hofmann
- arXiv Preprint No. 1806.00743
- On ill-posedness concepts, stable solvability and
saturation
- J. Inverse Ill-Posed Probl. 26(2):287–297, 2018
- with B. Hofmann
- arXiv Preprint No. 1709.01109
- The regularizing properties of the repeated midpoint
rule for weakly singular Volterra integral equations of the
first kind
- In New Trends in Parameter Identification for Mathematical Models, B. Hofmann, A. Leitao, J. Zubelli, (Eds.), Proc. Rio de Janeiro 2017, pp. 195–225, Birkhäuser, Basel 2018
- arXiv Preprint No. 1709.03142
- Optimal rates for Lavrentiev regularization with
adjoint source conditions
- Math. Comp. 87:785–80, 2018
- with B. Hofmann and P. Mathé
- Preprint
- Converse results, saturation and quasi-optimality for
Lavrentiev regularization of accretive problems
- SIAM J. Numer. Anal. 55(3):1315–1329, 2017
- Preprint
- The regularizing properties of multistep methods for
first kind Volterra integral equations with smooth kernels
- Comput. Methods Appl. Math. 17(1):139–159, 2017
- Preprint
- The regularizing properties of the composite
trapezoidal method for weakly singular Volterra integral
equations of the first kind
- Adv. Comput. Math. 36(2): 336–351, 2012
- Preprint
- Fractional multistep methods for weakly singular
Volterra equations of the first kind with noisy data
- Numer. Funct. Anal. Optim., 26(2):249–269,
2005.
- Preprint
- Numer. Funct. Anal. Optim., 26(2):249–269,
2005.
- The fast solution of integral and pseudo-differential
equations by GMRES
- Comput. Methods Appl. Math., 1(4):383–397, 2001
- with G. Vainikko (now University of Tartu,
Estonia)
- Preprint
- On the fast and fully discretized solution of integral
and pseudo-differential equations on smooth curves
- Calcolo 38(1):13–36, 2001
- with G. Vainikko (now University of Tartu, Estonia)
- Preprint
- The conjugate gradient method for linear ill-posed
problems with operator perturbations
- Numer. Algor. 20(1):1–22, 1999.
- The method of conjugate residuals for solving the
Galerkin equations associated with symmetric positive
semidefinite ill-posed problems
- SIAM J. Numer. Anal. 35(4):1621–1645, 1998.
- Preprint
- Resolvent estimates for Abel integral operators and the
regularization of associated first kind integral equations
- J. Integral Equations Appl. 9(3):253–278, 1997.
- The Galerkin scheme for Lavrentiev's m-times iterated
method to solve linear accretive Volterra integral
equations of the first kind
- BIT, 37(2):404–423, 1997
- On the discrepancy principle for iterative and
parametric methods to solve linear ill-posed problems
- Numer. Math., 75:99–120, 1996.
- The pseudo-optimality of parameter choices and stopping
rules for regularization methods in Banach spaces
- Numer. Funct. Anal. Optim., 17(2):181–195, 1996
- with U. Hämarik (Universität Tartu, Estonia)
-
Iterative and parametric methods for linear ill-posed
equations
- Habilitation thesis, Department of Mathematics, TU Berlin, 1995.
- On a minimax equality for seminorms.
- Linear Algebra Appl., 221:227–243, 1995
- with R.D. Grigorieff (TU Berlin)
- Die Effizienz des Diskrepanzprinzips für Verfahren vom
Typ der konjugierten Gradienten
- In E. Schock, Editor, Festschrift H. Brakhage, pp. 288–297, Aachen, 1994. Verlag Shaker.
- Two iterative schemes for solving linear
non-necessarily well-posed problems in Banach spaces
- In A.N. Tikhonov, Editor, Proc. Moscow 1991, pp. 134–143, VSP/de Gruyter, Utrecht, Tokyo, 1992.
-
Über die Diskretisierung und Regularisierung schlecht
gestellter Probleme
- PhD thesis, Department of Mathematics, TU Berlin, Berlin.
- Optimal algorithms for linear ill-posed problems yield
regularization methods
- Numer. Funct. Anal. Optim., 11(1-2):111–118, 1990.
- The instability of some gradient methods for ill-posed
problems
- Numer. Math., 58(1):129–134, 1990
- with B. Eicke and A.K. Louis
- Numer. Math., 58(1):129–134, 1990
- On the regularization of projection methods for solving
ill-posed problems
- Numer. Math., 57:63–79, 1990
- with G. Vainikko (University of Tartu, Estonia)
- On the regularization of the Ritz-Galerkin method for
solving ill-posed problems
- Acta et comment. Univers. Tartuensis , 863:3–18, 1989
- with G. Vainikko (University of Tartu, Estonia)
Short Papers and Surveys in Proceedings
- The solution of linear semidefinite ill-posed problems
by the method of conjugate residuals
- Proceedings of the International Conference on Operator Theory and its Applications to Scientific and Industrial Problems held October 7–11, 1998 in Winnipeg, Canada.
- The Lavrentiev-regularized Galerkin method for linear
accretive ill-posed problems
- Matimyas Matematika (Journal of the Mathematical Society of the Philippines), Special Issue (August 1998), pp. 57–66.
- Intern. Conf. Inverse Problems and Applications, Proc. Manila 1998.
- Lavrentiev's method for linear Volterra integral
equations of the first kind, with applications to the
non-destructive testing of optical-fibre preforms
- Mathematical Methods in Medical Imaging and Nondestructive Testing, Proc. Oberwolfach 1996, H.W. Engl, A.K. Louis und W. Rundell (Editors), pp. 196–211. Springer-Verlag, Wien, 1997.
- Preprint
- On the regularization of Abel's integral equation
- In O. Mahrenholtz und R. Mennicken, Editors, ICIAM/GAMM 95 Proceedings, Hamburg, Vol. 2, pp. 643–644, Akademie Verlag, Berlin, 1996.
- Some remarks concerning the stability of the method of
conjugate gradients for solving linear ill-posed problems
- In T. Meressoo, V. Poll, O. Vaarmann, und G. Vainikko, Editors, Numerical Methods and Optimization No. 3, Proc. Tallinn 1991, pp. 65–74, Estonian Academy of Sciences, Tallinn (Estonia), 1992.
- On the discretization and regularization of selfadjoint
ill-posed problems </ font>
- In P.C. Sabatier, Editor, Inverse Problems in Action, Proc. Montpellier 1989, pp. 117–121, Springer-Verlag, Berlin, New York, 1990.
Last update: 5.6.2017