Interpolation and Approximation of Functions

Syllabus
1. Kinds of:
- dependence and independence of functions,
- existence and definiteness of approximating functions,
- error of approximation.
2. Polynomial interpolation:
-the error estimate of the interpolation,
- Lagrangian and Mewton polynomials,
- extrapolation, interpolation of rational functions,
- choice of points for fitting.
3. Interpolating with a spline functions :
- interpolating with a cubic spline,
- features of cubic spline,
- B-spline curves,
- Bezier curves.
4. Orthogonal system of functions:
- orthogonal polynomials,
- Chebyshev, Hermitov, Gramov polynomials.
5. Least-squares approximations:
- the best L2- approximation, least-squares method,
- normal equations, solving sets of linear equations,
- algorithm of least-squares method,
- nonlinear data.
6. Chebyshev approximation:
- the best uniform approximation,
- algorithm of the method, maximum error.