The course covers the design and analysis of numerical algorithms for Matrix computations. Matrix computations consist the core of problems in the Computational Science and Technology. In particular the syllabus of the course is the following
- Error analysis for numerical computations.
- Numerical solution of linear systems. Direct (Gaussian Elimination, Gauss-Jordan, LU Decomposition) and Iterative methods (SOR, SSOR, PSD, Semi-Iterative and Conjugate Gradient).
- Numerical computation of Eigenvalues and Eigenvectors (Jacobi, Givens, LR, QR and Householder)
- Least Squares Problem.
- Numerical solution of Polynomial equations (Bernoulli, Quotient-Difference, Muller, Steffensen, Graffe’s and Bairstow) and Non Linear systems of equations (Newton and Newton-SOR).
- Introduction to the numerical solution of Partial Differential equations.