Subject: Special Topics in Numerical Analysis	Code: MC262	

Semester	 Hours: C+S+L	Type	 Section	
1	2+1+1	compulsory	Applied Mathematics	

Teaching Staff in Charge	Prof. COMAN Gheorghe, Ph.D., ghcoman@math.ubbcluj.ro	
Aims	An introduction in optimality problems with regard to the error, complexity and efficiency	
Content	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	
Selective References	1. COMAN GH.: Analiza numerica. Cluj-Napoca: Editura Libris, 1995.
2. STANCU D.D., COMAN GH., AGRATINI O., TRIMBITAS R.: Analiza numerica si teoria aproximarii. Vol. 1, Cluj-Napoca: Presa Universitara Clujeana, 2001.
3. STANCU D.D., COMAN GH., BLAGA P.: Analiza numerica si teoria aproximarii. Vol. 2, Cluj-Napoca: Presa Universitara Clujeana, 2002.
4. AGRATINI O., CHIOREAN I., COMAN GH., TRIMBITAS R.: Analiza numerica si teoria aproximarii. Vol. 3, Cluj-Napoca: Presa Universitara Clujeana, 2002.
5. COMAN GH., CATINAS T., BIROU M., OPRISAN A., OSAN C., POP I., SOMOGYI I., TODEA I.: Interpolation operators. Cluj-Napoca: Casa Cartii de Stiinta, 2004.
6. UEBERHUBER C.W.: Numerical Computation. Methods, software and analysis. Vol. 1,2, Berlin: Springer, 1997.
7. TRAUB F.J.: Iterative methods for the solution of equations. Englewood Cliffs: Pince-Hall, Inc., 1964.
8. TRAUB F.J., WONIAKOVSKI H.: A general theory of optimal algorithms. New York: Acad. Press, 1980. 	
Assessment	Exam