"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Special topics in numerical analysis
Hours: C+S+L
Matematică Aplicată
Teaching Staff in Charge
Prof. COMAN Gheorghe, Ph.D., ghcoman@math.ubbcluj.ro
This course approaches the theory of real functions by using linear operators including various methods of generalization as well as the study of the convergence of operators sequences. The rate of convergence is studied and some asymptotic formulas are established. It also surveys their behaviour on subspaces of functions and investigates their major properties.
Moduli of smoothness, K-functionals and summation methods are also presented. The theory is illustrated through Bernstein - type operators, convolution operators and Kanto-rovich and Durrmeyer type generalizations. The course also deals with the probabilistic study of some semigroups of operators.
1. O. AGRATINI, Aproximare prin operatori liniari, Presa Universitara Clujeana, 2000.
2. O. AGRATINI, Positive Approximation Processes, Hiperboreea Press, 2001.
3. F. ALTOMARE, M. CAMPITI, Korovkin-Type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, Vol. 17, Walter de Gruyter & Co., Berlin, New York, 1994.
4. G.A. ANASTASSIOU, S.G. GAL, Approximation Theory Moduli of Continuity and Global Smoothness Preservation, Birkhauser, Boston, Basel, Berlin, 2000.
5. Gh. COMAN, Analiza numerica, Editura Libris, Cluj-Napoca, 1995.
6. Y. DITZIAN, V. TOTIK, Moduli of Smoothness, Springer Series in Computational Mathematics, Vol. 9, Springer-Verlag, New York Inc., 1987.
7. S. KARLIN, Total Positivity, Vol.1, Stanford Univ. Press, Stanford, California, 1968.
8. I. MUNTEAN, Analiza Functionala, Univ. „Babes-Bolyai", Fac. de Mat. si Informatica, Cluj-Napoca, 1993.
9. G.-C. ROTA, D. KAHANER, A. ODLYZKO, On the Foundations of Combinational Theory VIII. Finite operator calculus, Journal of Math. Analysis and Applications, 42 (1973), 685-760.
10. D.D. STANCU, Gh. COMAN, O. AGRATINI, R. TRIMBITAS, Analiza numerica si teoria aproximarii, Vol. 1, Presa Universitara Clujeana, Cluj-Napoca, 2001.