Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MC262	Special Topics in Numerical Analysis	

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

Teaching Staff in Charge	Lect. CATINAS Teodora Maria, Ph.D., tcatinas@math.ubbcluj.ro	
Aims	The study of some modern procedures of approximation and interpolation, numerical integration and of solving nonlinear equations, with emphasize on optimality and efficiency.	
Content	There are studied spline interpolation operators (of Lagrange, Hermite and Birkhoff type) and univariate and bivariate Shepard interpolation operators (of Lagrange, Hermite, Birkhoff, Abel-Goncharov, Lidstone and Bernoulli type). Also, there are studied interpolation operators on simplex and rectangular domains. There are presented the properties of these operators and there are studied the approximation errors. 
There are presented the optimal quadrature formulas in sense of Sard and Nikolski, and homogenous cubature formulas.
There are studied the succesive approximation method and Newton method for nonlinear systems.
Also, the course deals with the efficiency of the quadrature formulas and of the numerical methods for solving nonlinear equations.	
Bibliography	1.	O. Agratini, P. Blaga, Gh. Coman, Lectures on Wavelets, Numerical Methods, and Statistics, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005. 
2.	O. Agratini, I. Chiorean, Gh. Coman, R.T. Trîmbitaş, Analiză Numerică şi Teoria Aproximării, vol. III, Presa Universitară Clujeană, 2002; 
3.	T. Cătinaş, Interpolation of scattered data,  $Casa Carţii de Ştiinţă$,  2007.
4.	Gh. Coman, Analiză numerică, Ed. Libris, Cluj-Napoca, 1995.
5.	Gh. Coman, T. Cătinaş, şi alţii, Interpolation operators,  $Casa Carţii de Ştiinţă$, Cluj-Napoca, 2004.
6.	Gh. Coman, I. Chiorean, T. Cătinaş, Numerical Analysis. An Advanced Course,  Presa Universitară Clujeană, 2007.
7.	D.D. Stancu, Gh. Coman, O. Agratini, R. Trimbitas, Analiză Numerică şi Teoria Aproximării, vol. I, Presa Universitară Clujeană, 2001;
8.	D.D. Stancu, Gh. Coman, P. Blaga, Analiză Numerică şi Teoria Aproximării, vol. II, Presa Universitară Clujeană, 2002; 
9.	R. Trîmbitaş, Numerical Analysis, Presa Universitară Clujeană, 2007

Assessment	exam