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

SUBJECT

Code
Subject
MMC1009 Numerical Methods in Simulation
Section
Semester
Hours: C+S+L
Category
Type
Modeling and Simulation - in English
3
2+1+1
speciality
compulsory
Teaching Staff in Charge
Assoc.Prof. TRÎMBITAS Radu Tiberiu, Ph.D.,  tradumath.ubbcluj.ro
Aims
To learn student to apply Numerical Analysis techniques to Simulation
Content
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 – 3D, Volume Visualization, Animation
· ODE Solvers - one-step, multistep, stiffness, event-handling
References
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%
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject