Numerical methods

Basic problems of the numerical mathematics, errors in computations. Solving of
equation f(x)=0: bisection method, regula-falsi, iterative method, Newton´s
iteration, roots of polynomials. Numerical solution of systems of linear
algebraic equations: LU-factorization, iterative methods, condition number of
matrix, ill-conditioned matrices. Numerical solution of systems of nonlinear
equations: Fixed-point iteration, Newton’s method. Interpolation and
approximation of functions: Polynomial interpolation, interpolation by cubic
spline functions, least squares approximation. Numerical integration: Trapezoid
rule, Simpson’s rule, Richardson extrapolation, Monte Carlo method.