Polynomiální interpolace po částech

Abstract

Polynomial interpolation can be used to approximate a function or to create a polynomial that agrees with some information about a function (for example discrete values obtained by some measurement). There may be cases in which the interpolation error is too large. In these situations piecewise polynomial interpolation is a suitable alternative. This method consists of dividing the interval in which the function is interpolated into several subintervals. Subsequently, polynomial interpolation is performed on each subinterval so that the resulting approximating function is continuous. The goal of this thesis is to study and elaborate on the topic of Lagrange and Hermite interpolation as well as on piecewise polynomial interpolation. An important part of the thesis is also the presentation of solutions to suitable and interesting problems related to this topic.