In this thesis we present the solution to four-point parabolic interpolation problem. The theorem that shows how the number of interpolation curves is related to the shape of the quadrilateral that has the given points as its vertices is proven and the construction of the interpolant in some practical examples is described. The same problem is solved again with a different approach, that is with cubic Lagrange polynomials. We find such parameters that lower the interpolant’s degree to obtain a parabolic curve. Furthermore, the Hermite’s problem is discussed, where we find a parabolic interpolant for two points and two tangent vectors. Lastly, we numerically calculate the convergence rate for approximation of parametrically given curves with parabolic curves.
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