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Publikationsliste Plato

Publications Dr. Robert Plato, Department of Mathematics, Siegen University


Textbooks

  • Numerische Mathematik kompakt -- Grundlagenwissen für Studium und Praxis
    • 4. Auflage, Verlag Vieweg+Teubner, 2010. xvi+426 S. ISBN 978-3-8348-1018-2
  • 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

  • Convergence results and low order rates for nonlinear Tikhonov regularization with oversmoothing penalty term
  • A regularized variational inequality approach for nonlinear monotone ill-posed equations
  • On ill-posedness concepts, stable solvability and saturation
  • 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
  • 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)
  • 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.
  • 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
  • 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