Wednesday, March 26, 2008

Course description 6

19. Matrix Theory

Matrix analysis, general linear systems, special linear systems, linear space and linear transformation, orthogonalization and least squares. The unsymmetric eigenvalue problem, the symmetric eigenvalue problem. Iterative methods for linear systems, reductions and transformations. Methods for the dominant eigenvalue. Methods for the subdominant eigenvalue. Inverse iteration. Jacobi's methods, Givens and Householder's methods. Eigensystem of a symmetric tridiagonal matrix. The LR and QR algorithms. Extensions of Jacobi's method, extension of Givens' and Householder's methods. QR Algorithm for Hessenberg matrices. SOR method and related methods.

20. Visual C++

Short description ,basic facilities. Design using C++, variables and basic types, library types, arrays and pointers, functions, algorithms, tools for large programs, specialized tools and techniques.

21. Partial Differential Equations

Short description, basics of functional analysis. Lax-Milgram lemma, Sobolev spaces, Galerkin methods, the finite element method, basic features, convergence analysis for 1D problems. Error control, a-priori and a-posteriori analysis. Advection-diffusion problems. Stabilization techniques, Galerkin Generalized schemes for boundary layer problems. Parabolic problems. Space-time approximations with finite elements and finite differences. Hyperbolic (convection) problems. conservative finite difference schemes for scalar problems. Continuous and discontinuous finite elements.

22. MATLAB 2

Short description , mainstream areas of image processing. intensity transformations, linear and nonlinear spatial filtering, filtering in the frequency domain, image restoration and registration, color image processing, image data compression, morphological image processing, image segmentation, region and boundary representation and description, and object recognition. Solve image processing problems using MATLAB and IPT functions. New function was written and documented , implement new image processing software solutions.

23.The information science and foundation

Short description, entropy,relative entropy and mutual information, entropy rates of stochastic process, channel capacity, differential entropy, the Gaussian channel, information theory, coding, channel coding theorem.

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