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

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.

Keywords

• continued fraction
• rational thiele-hermite interpolation
• recurrence formulas