This topic includes: Representation of numbers, computer numbers, rounding, computer arithmetic; sources of error, their classification and analysis. Iterative algorithms, tolerance, stopping conditions. Introduction to Matlab. Order and rage of convergence. Solving f(x) = 0 (bisection, secant, regular falsi, Newton). Interpolation (Lagrange, Hermite polynomials, divided differences, cubic splines). Numerical differentiation. Numerical integration, trapezoidal and Simpson formulas, error estimates, Legendre polynomials, Gaussian quadrature, double and triple integrals. Gaussian Elimination Algorithm and its applications, pivoting strategies, complexity, LU factorisation. Special matrices and GEA (diagonally dominant, self-adjoint, positive definite, unitary, banded). Matrix norms, spectral radius. Iterative methods (Jacobi, Gauss-Seidel, SOR). Eigenvalues and eigenvectors, basic spectral mapping theorem, power, symmetric power, and inverse power methods. Jacobi matrix and its properties, Newton's method for nonlinear systems. Numerical methods for ordinary differential equations (ODE's) and systems of ODE's (Euler, Taylor and Runge-Kutta methods), stiff ODE's.
This topic aims to provide:
Timetable details for 2021 are no longer published.