The course provides an introduction to Numerical Linear Algebra, including:
Matrices, Eigenvalues, Norms, Spectral Radius, Condition Number, and Basic Stability Estimates.
Basic Methods:
Computational techniques based on the GEM, error estimates, stability, pivoting, implementation, factorizations (LU, Cholesky, QR).
Iterative Methods:
Basic definitions and general theory, Jacobi, Gauss-Seidel methods, relaxation techniques (JOR, SOR), Richardson iteration schemes, gradient/descent methods, Conjugate Gradient Method, introduction to Arnoldi, Krylov, GMRES methods.
Eigenvalues-Eigenvectors Computation:
Introduction to geometrical properties of eigenvalues, basic stability estimates, power method, QR, Householder, Givens, Lanczos methods.
Nonlinear Systems:
Introduction to iterative schemes, Newton-Raphson, implementation.
- Teacher: Κωνσταντινος Χρυσαφινος
ECTS : 5
Language : el