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

SYLLABUS

I. General data
Code	Subject	
MMC1009	Numerical Methods in Simulation	

Semester	Hours: C+S+L	Category	Status	
3	2+2+0	speciality	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 form skills on numerical methods for graduate students, with orientation in simulation and to apply numerical linear algebra methods to simulation, to implement methods and solutions in MATLAB	

IV. Course contents
Linear algebra basics, SVD, Least squares problems, Numerical solution of linear algebraic systems, eigenvalues and eigenvectors, randomized algorithms
MATLAB: 3D Graphics, Volume Vizualization Techniques, Numerical Linear Algebra in MATLAB, sparse matrices	

V. Bibliography
1.	L. N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, Philadelphia, 1997
2.	J. W. Demmel: Numerical Linear Algebra, SIAM 1997
3.	G. Golub and C. Van Loan: Matrix Computations. Johns Hopkins University Press, Baltimore, 3rd edition, 1996
4.	R. Trîmbiţaş: Numerical Linear  Algebra – electronic lecture notes http://www.math.ubbcluj.ro/~tradu
5.	Mathworks Inc: MATLAB set of manuals
6.	R. Motwani, P. Raghavan: Randomized Algorithm, Cambridge University Press, 1995	

VI. Thematic of didactic activities per weeks
Basics of Linear Algebra – 1 lecture (matrix-vector and matrix-matrix product, matrix-norms, orthogonality, unitary and orthogonal matrices [1, 2, 3])
Singular Value Decomposition (SVD) – 1 lecture [1, 4]
QR- decomposition and Least Squares Problem – 1 lecture [1, 2, 4]
Floating point arithmetic, conditioning and stability 1 lecture [1, 4]
Direct Methods for Linear Algebraic Systems - 1 lecture (Gaussian elimination, Cholesky decomposition, their stability) [1, 2, 3, 4]
Eigenproblems – 3 lectures  (eigenvalues and eigenvectors, properties two-phase eigenvalue computation, Hessenberg reduction - 1 lecture,  nonsymmetric eigenvalue problems, QR algorithm  – 1 lecture, symmetric eigenvalue problems and SVD computing – 1 lecture) [1, 2, 3, 4] 
Iterative Metods for Linear Algebraic Systems – 3 lectures (introduction, stationary methods – 1 lecture, Krylov subspace methods, Arnoldi and Lanczos iteration,  GMRES -1 lecture, CG  and preconditioning – 1 lecture) [1, 2, 3, 4]
Sparse Matrices; Numerical Linear Algebra Software – 1 lecture [2, 3]
Randomized Algorithms – 2 lecture [6]
For seminars / labs: MATLAB: 3D Graphics, Volume Vizualization Techniques, Numerical Linear Algebra, sparse matrices [5]	

VII. Didactic methods used
Magister’s lecture, lecture with demos, electronic-device-based demonstration, case study, individual study	

VIII. Assessment
Exam: written test 50% + practical test 50%	

IX. Additional references
1.	Y. Saad : Numerical Methods for Large Eigenvalue Problems, Manchester University Press, Manchester, UK, 1992, available also via www, personal web page of author, http://www-users.cs.umn.edu/~saad 
2.	Y. Saad : Numerical Methods for Sparse Linear Systems, SIAM, 1993, first edition available also via www, http://www-users.cs.umn.edu/~saad
3.	N. Higham : Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996
4.	D. Goldberg: What every computer scientist should know about floating point arithmetic, ACM Computing Surveys, , 23:5-48, 1991,  available also via www, http://cch.loria.fr/documentation/IEEE754/ACM/goldberg.pdf or http://grouper.ieee.org/groups/754/

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