MC262 | Special Topics in Numerical Analysis |
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 |