Lectures:
Introduction to MATLAB (overview of toolboxes and functions, help, basic elements, editing of the n-dimensional arrays).
MATLAB programming (control flow statements, 2D and 3D graphics).
Advanced MATLAB functions (graphical user interface).
Analytic geometry (computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures (band, profile, row compressed, column compressed).
Solution of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Gauss elimination (row and column versions, pivotization).
LU and Choleski decomposition (row and column versions, pivotization).
Reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
QR decomposition (Givens and Householder transforms).
Eigenvalues and spectral decomposition (QR and LR algorithms, shift).
Singular decomposition, pseudoinverse.
Lanczos method and conjugate gradient method.
Project presentation.
Exercises:
Introduction to MATLAB, functions overview, editing of the n-dimensional arrays.
MATLAB programming techniques, the use of the control flow statements, 2D and 3D graphic functions).
Graphical user interface implementation.
Computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures implementation (band, profile, row compressed, column compressed).
Solvers of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Solution of the linear algebraic system using Gauss elimination (row and column versions, pivotization).
Solution of the linear algebraic system using LU and Choleski decomposition (row and column versions, pivotization).
Application of the reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
The use of the QR decomposition (implementation, Givens and Householder transforms, applications).
Computation of the eigenvalues and spectral decomposition (implementation, QR and LR algorithms, shift, applications).
Computation of the singular decomposition and pseudoinverse (implementation, application).
Lanczos method and conjugate gradient method (implementation, applications).
Project presentation.
Projects:
Application oriented project in MATLAB (max. 30 points).
Introduction to MATLAB (overview of toolboxes and functions, help, basic elements, editing of the n-dimensional arrays).
MATLAB programming (control flow statements, 2D and 3D graphics).
Advanced MATLAB functions (graphical user interface).
Analytic geometry (computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures (band, profile, row compressed, column compressed).
Solution of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Gauss elimination (row and column versions, pivotization).
LU and Choleski decomposition (row and column versions, pivotization).
Reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
QR decomposition (Givens and Householder transforms).
Eigenvalues and spectral decomposition (QR and LR algorithms, shift).
Singular decomposition, pseudoinverse.
Lanczos method and conjugate gradient method.
Project presentation.
Exercises:
Introduction to MATLAB, functions overview, editing of the n-dimensional arrays.
MATLAB programming techniques, the use of the control flow statements, 2D and 3D graphic functions).
Graphical user interface implementation.
Computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures implementation (band, profile, row compressed, column compressed).
Solvers of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Solution of the linear algebraic system using Gauss elimination (row and column versions, pivotization).
Solution of the linear algebraic system using LU and Choleski decomposition (row and column versions, pivotization).
Application of the reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
The use of the QR decomposition (implementation, Givens and Householder transforms, applications).
Computation of the eigenvalues and spectral decomposition (implementation, QR and LR algorithms, shift, applications).
Computation of the singular decomposition and pseudoinverse (implementation, application).
Lanczos method and conjugate gradient method (implementation, applications).
Project presentation.
Projects:
Application oriented project in MATLAB (max. 30 points).