Syllabus
Aproximations of functions in R, Lagrange interpolation polynomial, error of Lagrange interpolation, cubic spline, construction of natural cubic spline.
Numerical integration of functions, Newton-Cotes formulae, composed Newton-Cotes formulae, Romberg quadrature, Gauss quadrature.
Methods for solution of nonlinear equations, Newton method, proof of convergence of Newton method, method of successive approximations for nonlinear equations, roots of polynomial, Horner scheme.
Systems of linear equations, condition number of matrices, Gauss' elimination, LU decomposition, influence of rounding errors, Cholesky decomposition, QR decomposition, iterative methods for the solution of systems of linear equations.
Computation of matrix eigenvalues.
Numerical integration of ordinary differential equations. One-step methods, Runge-Kutta methods.
Gradient methods.
Annotation
The first course of numerical analysis for students of computer science. Topics: approximaton of continuous functions, numerical qudrature, differentiation and methods for solving ordinary differential equations, methods of numerical linear algebra - decomposition of matrices, solving systems of linear equations, eigenvalue problem.
Introduction to numerical methods for solving partial differential equations.