Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare şi simulare
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MC271	Numeric Methods in Simulation	

Semester	Hours: C+S+L	Category	Status	
2	2+2+1		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
TRÎMBITAS Radu Tiberiu	Ph.D.	Assoc.Prof.	Numerical and Statistical Calculus	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
To learn student to apply Numerical Analysis techniques to Simulation

IV. Course contents
Numerical Linear Algebra
Matrix Analysis - matrix norms, sequences of matrices
Singular Value Decomposition (SVD), properties, applications
Orthogonality, QR Decomposition, Householder reflections, Givens rotations,    applications to Least Squares Problems, SVD and least squares
Condition of a problem and of an algorithm, Floating Point Arithmetic, machine epsilon, cancelation, IEEE standard, Stability and Backward Stability
Direct Methods for Linear Algebraic Systems: GEPP, Cholesky
Eigenvalues and Eigenvectors, properties, power method, inverse iteration, QR. Symmetric eigenvalue problems.
Stationary Iterative Methods for  Linear Algebraic Systems: Jacobi, Gauss-Seidel, SOR
Nonstationary Iterative Methods for  Linear Algebraic Systems: conjugate gradient, GMRES, BICG
Iterative Methods for Eigenvalues and Eigenvectors: Arnoldi, Lanczos
Sparse Matrices - representation, operations, algorithms, black boxes
 
MATLAB
Sparse Matrices in MATLAB
Numerical Linear Algebra in MATLAB: systems, least squares, eigenvalues and eigenvectors, SVD
MATLAB Graphics &#8211; 3D, Volume Visualization, Animation
ODE Solvers - one-step, multistep, stiffness, event-handling

V. Bibliography
1. Demmel, James - Applied Numerical Linear Algebra, SIAM, 1997
2. Agratini, Octavian, Chiorean, Ioana, Coman, Gheorghe, Trimbitas, Radu,- Analiza numerica si Teoria aproximarii, vol. III, Presa Universitara Clujeana, 2002
3. Trefethen, Lloyd N., Bau III, David, - Numerical Linear Algebra, SIAM, 1997

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Exam 40%, Practical exam 40%, semester activity 20%	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. TRÎMBITAS Radu Tiberiu, Ph.D.