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

Code	Subject	
MMC1009	Numerical Methods in Simulation	

Section	Sem.	Hours: C+S+L	Category	Type	
Modeling and Simulation  - in English	3	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. TRÎMBITAS Radu Tiberiu, Ph.D., tradu@math.ubbcluj.ro	
Aims	To learn student to apply Numerical Analysis techniques to Simulation
	
Content	Numerical Linear Algebra

&#183;       Matrix Analysis - matrix norms, sequences of matrices
&#183;       Singular Value Decomposition (SVD), properties, applications
&#183;       Orthogonality, QR Decomposition, Householder reflections, Givens rotations,    applications to Least Squares Problems, SVD and least squares
&#183;       Condition of a problem and of an algorithm, Floating Point Arithmetic, machine epsilon, cancelation, IEEE standard, Stability and Backward Stability
&#183;       Direct Methods for Linear Algebraic Systems: GEPP, Cholesky
&#183;       Eigenvalues and Eigenvectors, properties, power method, inverse iteration, QR. Symmetric eigenvalue problems.
&#183;       Stationary Iterative Methods for  Linear Algebraic Systems: Jacobi, Gauss-Seidel, SOR
&#183;       Nonstationary Iterative Methods for  Linear Algebraic Systems: conjugate gradient, GMRES, BICG
&#183;       Iterative Methods for Eigenvalues and Eigenvectors: Arnoldi, Lanczos
&#183;       Sparse Matrices - representation, operations, algorithms, black boxes

MATLAB

&#183;       Sparse Matrices in MATLAB
&#183;       Numerical Linear Algebra in MATLAB: systems, least squares, eigenvalues and eigenvectors, SVD
&#183;       MATLAB Graphics &#8211; 3D, Volume Visualization, Animation
&#183;       ODE Solvers - one-step, multistep, stiffness, event-handling
	
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
	
Assessment	Exam 40%, Practical exam 40%, semester activity 20%