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

SUBJECT

Code
Subject
MMC1002 Special Topics in Numerical Analysis
Section
Semester
Hours: C+S+L
Category
Type
Applied Mathematics
2
2+2+0
speciality
compulsory
Teaching Staff in Charge
Lect. CATINAS Teodora Maria, Ph.D.,  tcatinasmath.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.
References
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
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject