Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMC1009 | Numerical Methods in Simulation |
| 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 |
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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 |