Theodoula N. Grapsa Associate Professor,
Department of Mathematics, University of Patras, Greece.

Selected Publications:

● Grapsa T.N. and Vrahatis M.N., A dimension-reducing method for solving systems of non linear equations in R n, International Journal of Computer Mathematics 32, pp. 205-216, 1990.

● Grapsa T.N., Vrahatis M.N. and Bountis T.C., Solving systems of nonlinear equations in Rn using a rotating hyperplane in Rn+1, International Journal of Computer Mathematics 35, pp. 133-151, 1990.

Vrahatis M.N., Ragos O., Skiniotis T., Zafiropoulos F.A. and Grapsa T.N., RFSFNS: A portable package for the numerical determination of the number and the calculation of roots   of Bessel functions, Computer Physics Communications, 92, 252-266, 1995.

Androulakis G.S., Vrahatis M.N. and Grapsa T.N., Studying the performance of optimization methods by visualization, In: 8th System Modelling Control,Vol. 1, E. Kacki ed., Lodz, pp. 60 - 65, 1995.

● Grapsa T.N., Vrahatis M.N. and Androulakis G.S., A composite dimension - reducing method for unconstrained optimization, In: 8th System Modelling Control, Vol. 1, E. Kacki ed., Lodz, pp. 392-297, 1995.

●  Vrahatis M.N., Grapsa T.N. and Androulakis G.S., Rapid composite dimension-reducing methods for unconstrained optimization, In: 8th System Modelling Control, Vol. 2, E. Kacki ed., pp. 363-368, Lodz, 1995.

● Grapsa T.N. and Vrahatis M.N., A dimension - reducing method for unconstrained optimization, Journal of Computational and Applied Mathematics, 66, 239 - 253, 1996.

Magoulas G.D., Vrahatis M.N., Grapsa T.N. and Androulakis G.S., Neural network supervised training based on a dimension reducing method, in Mathematics of Neural Networks: Models, Algorithms & Applications, In: Mathematics of Neural Networks, Models, Algorithms and Applications, S.W. Ellacott, J.C. Mason and I.J. Anderson eds., Kluwer Academic Publishers, Boston, 1997, Chapter 41, pp.245-249

Magoulas G.D., Vrahatis M.N., Grapsa T.N. and Androulakis G.S., A training method for discrete multilayer neural networks, In: Mathematics of Neural Networks, Models, Algorithms and Applications, S.W. Ellacott, J.C. Mason and I.J. Anderson eds., Kluwer Academic Publishers, Boston, 1997, Chapter 42, pp.250-254.

● Grapsa T.N., Androulakis G.S. and Vrahatis M.N., An inexact dimension reducing method for solving systems of nonlinear equations, In: Proceeding of the 2nd IMACS International Conference on: "Circuits, Systems and Computers" (IMCAS-CSC'98), 1998, Vol. 1, pp. 66-71. Also In: Recent Advances in Circuits and Systems, N.E. Mastorakis ed., World Scientific Publishing Co. Pte. Ltd., pp. 315-320, 1998.

Grapsa T.N., Androulakis G.S. and Vrahatis M.N., An inexact dimension reducing method for solving systems of nonlinear equations, In: Proceedings of Recent Advances in Circuits and Systems, N.E. Mastorakis ed., World Scientific Publishing, 1998, pp. 315-320. Also In: Proceedings of the 2nd IMACS International Conference on: "Circuits, Systems and Computers" (IMACS-CSC'98), Vol. 1, N.E. Mastorakis ed., Athens, Greece, 1998, pp. 66-71. Also In: Recent Advances in Circuits and Systems, N.E. Mastorakis ed., World Scientific Publishing Co. Pte. Ltd., 1998, pp.315-320.

Dimitris G. Sotiropoulos and Theodoula N. Grapsa. A branch-and-prune method for global optimization: The univariate case. In: Scientific Computing, Validated Numerics, Interval Methods, W. Kraemer and J.W.v.Gudenberg eds., pp. 215-226, Kluwer, Boston, 2001.

● G.E. Manoussakis, D.G. Sotiropoulos, C.A. Botsaris and T.N. Grapsa, A Non - Monotone Conic Method for Unconstrained Optimization. In: Proceedings of 4th GRACM Congress on Computational Mechanics (GRACM2002), Prof. Demos T. Tsahalis ed., Vol. I, pp. 172-179, 2002.

D.G. Sotiropoulos, A.E. Kostopoulos and T.N. Grapsa, A Spectral Version of Perry's Conjugate Gradient Method for Neural Network Training. In: Proceedings of 4th GRACM Congress on Computational Mechanics (GRACM2002), Prof. Demos T. Tsahalis ed., Vol. I, pp. 291-298, 2002.

D.G. Sotiropoulos, J. A. Nikas and T.N. Grapsa, Improving the Efficiency of a Polynomial System Solver via a Reordering Technique. In: Proceedings of 4th GRACM Congress on Computational Mechanics (GRACM2002), Prof. Demos T. Tsahalis ed., Vol. III, pp. 970-976, 2002.

T.N. Grapsa and M.N. Vrahatis, Dimension Reducing Methods for Systems of Nonlinear Equations and Unconstrained Optimization: A Review. Recent Advances in Mechanics and Related Fields: Special Volume in Honour of Professor Constantine L. Goudas, pp. 215-225, 2003.

A.E. Kostopoulos, D. Glotsos, P. Spyridonos, G. Nikiforidis, D. Sotiropoulos and T. Grapsa, Comparative Evaluation of Feedforward and Probabilistic Neural Networks for the Automatic Classification of Brain Tumours. Ιn: Proceedings of the 1st International Conference 'From Scientific Computing to Computational Engineering', Prof. Demos T. Tsahalis ed., ISBN 960-530-069-9, VOL. I, PP. 309-315, 2004.

D.G. Sotiropoulos, A. E. Kostopoulos, and T.N. Grapsa, Training Neural Networks using Two - Point Stepsize Gradient Methods. In ICNAAM - International Conference of Numerical Analysis and Applied Mathematics 2004: Proceedings, T.E. Simos and Ch. Tsitouras ed., pp. 356-359, Willey-VCH Verlag GmbH and Co., Weinheim, ISBN: 3-527-40563-1, 2004.

D. G. Sotiropoulos and T.N. Grapsa, Optimal Centers in Branch - and - Prune Algorithms for Univariate Global Optimization, Applied Mathematics and Computation, Vol. 169(1), pp. 247-277, 2005.

● T.N. Grapsa, Minimal root finder in interval global optimization. In Proceedings of ICNAAM - International Conference of Numerical Analysis and Applied Mathematics, T.E. Simos, G. Psihoyios, C. Tsitouras (eds), Willey-VCH, ISBN: 3-527-40563-X, 2006.

I.A. Nikas, D.G. Sotiropoulos and T.N. Grapsa, Extending Interval Newton Method for Nonlinear Parameterized Equations. In: Proceedings of International Conference of Numerical Analysis and Applied Mathematics (ICNAAM-2006), T.E. Simos, G. Psihoyios, C. Tsitouras (eds), Willey-VCH, ISBN: 3-527-40563-X, pp.512-513, 2006.

● T.N. Grapsa, E.N. Malihoutsaki, A Newton's method without direct evaluation of nonlinear function values. In: Proceeding of the 8th Hellenic European Conference on Computer Mathematics and its Applications (HERCMA'2007), E.A. Lipitakis ed., 2007.

I.A. Nikas and T.N. Grapsa, On solving Efficiently Interval Polynomial Equations of Degree n over R. In: Proceedings of Conference in Numerical Analysis, Recent Approaches to Numerical Analysis, Theory, Methods and Applications (Honoring Richard S. Varga on his 80th birthday) (NumAn2008), E. Gallopoulos, E. Houstis, I.S. Kotsireas, D. Noutsos and M.N. Vrahatis ed., 2008.

A. E. Kostopoulos and T. N. Grapsa, Self-Scaled Conjugate Gradient Training Algorithms, Neurocomputing, Vol. 72, No. 13-15, pp. 3000-3019, 2009.

I. A. Nikas and T. N. Grapsa, Bounding the Zeros of an Interval Equation, Applied Mathematics and Computation, 213 (2009), pp. 466-478.

E. N. Malihoutsaki, I. A. Nikas and T. N. Grapsa, Improved Newton's method without direct function evaluations, Journal of Computational and Applied Mathematics, Vol. 227(1), pp. 206-212, 2009.

Eleftheria N. Malihoutsaki, George S. Androulakis and T.N. Grapsa, A novel Forecasting Hybrid Method for Unconstrained Optimization, in: Proceedings of 24th Mini EURO Conference on Continuous Optimization and Information-Based Technologies in The Financial Sector, Izmir, Turkey, June 23-26, pp. 76-80, 2010, ISBN: 978-9955-28-598-4.

Eleftheria N. Malihoutsaki, George S. Androulakis and T.N. Grapsa, A new approach for solving systems of nonlinear equations via a forecasting hybrid technique, in Proc. Recent Approaches to Numerical Analysis: Theory, Methods and Applications (NumAn2010), V. Dougalis, E. Gallopoulos, A. Hadjidimos, D. Noutsos, Y. Saridakis, and M. N. Vrahatis, Eds., Chania, Crete, Greece, Sept. 15-18, pp. 143-148, 2010. 

● Theodoula N. Grapsa, On variable priorities for solving systems of nonlinear equations, In: Proceedings of the 1st International Symposium & 10th Balkan Conference on Operational Research, Thessaloniki, Greece, ISBN 978-960-27277-7-9, pp. 256–262, 2011.

Christina D. Nikolakakou, Theodoula N. Grapsa and George S. Androulakis, Integrating Taylor’s expansion on the lexicographic approach for unconstrained optimization, In Proceedings of the 1st International Symposium & 10th Balkan Conference on Operational Research, Thessaloniki, Greece, ISBN 978-960-27277-7-9, pp. 354–361, 2011.

● Theodoula N. Grapsa A modified Newton direction for unconstrained optimization, Optimization , vol. ahead-of-p, no. ahead-of-p, pp. 1-22, 2012.

Christina D. Nikolakakou, Theodoula N. Grapsa, Ioannis A. Nikas and George S. Androulakis, "A sequential approach for unconstrained optimization via a partitioning technique", International Journal of Computer Mathematics, 2014, DOI: 10.1080/0027160.2014.907403.


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