A certain method of construction of Thiele-Hermite continued fraction at a point

Author:

Pahirya MykhailoORCID,Myslo YuliiaORCID

Abstract

The problem of interpolation of the function of a complex variable at a point of a compact set by the Thiele-Hermite continued fraction is investigated. Formulas for calculating the coefficients of the continued fraction based on values of the function and its derivates at a point are obtained. Several examples of computations are provided.

Publisher

Odesa National University of Technology

Subject

Applied Mathematics,Geometry and Topology,Analysis

Reference10 articles.

1. [1] F. Gerrish. 64.2 A useless formula? The Mathematical Gazette, 64(427):52-52, 1980. doi:10.2307/3615888.

2. [2] W. B. Jones and W. J. Thron. Continued fractions, volume 11 of Encyclopedia of Mathematics and its Applications. Addison-Wesley Publishing Co., Reading, MA, 1980. Analytic

3. theory and applications, With a foreword by Felix E. Browder, With an introduction by Peter Henrici.

4. [3] Yu. Myslo and M Pahirya. Osculatory interpolating Thiele continued fraction. Proceedings of the International Geometry Center, 15(2):138-160, 2022. doi:10.15673/tmgc.v15i2.2296.

5. [4] N. E. Nörlund. Vorlesungen über Differenzenrechnung. Berlin: Springer, 1924. doi:10.1007/978--3--642--50824--0.

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