Nuno Filipe Marcelino Martins
Weekly - 4
Total - Available soon
1. Introduction to Numerical Analysis. Errors. Conditioning of a problem and
stability of a method.
2. Interpolation and Function Approximation: Polynomial interpolation, trigonometric interpolation, cubic spline interpolation, least squares approximation.
3. Numerical Integration: Newton-Cotes integration formulas, Gaussian integration.
4. Root finding for Nonlinear Equations: Bisection method, fixed-point iteration method, Newton’s method and secant method.
5. Numerical Linear Algebra: Norms of vectors and matrices, conditioning of a system, direct methods for the solution of systems of linear equations, eigenvalues and eigenvectors, Gershgorin’s theorem. Iterative methods for computing eigenvalues and eigenvectors. Iterative methods for solving a linear system of equations.
Programs where the course is taught: