Piecewise rational interpolation by witch of Agnesi (Q2403106)

The paper deals with the problem of piecewise rational interpolation with a special type of the Italian mathematician M. G. Agnesi. The curve is given by a rational function with one parameter. Next, the author generalizes this function by introducing some additional parameters. The number of parameters is extended from one to four. Furthermore, the author proves two theorems. The first one states that we can find at least one generalized Agnesi curve passing through two different points and the second one that a generalized curve of Agnesi exists that passes through two different points and with the given values of the first derivative at the ends of the considered interval. After the theorems examples showing construction of such curves are presented. Then, an estimation of the error of interpolation on a given interval is made. Using the generalized curve of Agnesi, the author next proposes an algorithm for the piecewise rational interpolation method and presents some examples showing the use of the proposed algorithm.