On Several Questions About Continued Fraction

Main contents of this thesis are listed as follows:In chapter one, the relevant literature is briefly survey.In chapter two, we discuss the existence questions of Thiele-type rational interpolants. One of important constructing elements of Thiele-type rational interpolating algorithm is inverse difference, the existence conditions of which are analyzed. Furthermore, we analysis the appearance of unattainable points when inverse difference exists, and the results we get are of clear geometric significance.In chapter three, the truncation error of a set of limited periodic continued fractions was obtained by use of backward three term recurrence relations.In Computer Aided Geometric Design, curves and surfaces generally have two kinds of representations: parametric one and implicit one. Comparing with the former, the latter has special advantages. In Chapter four, we present a new implicitizing algorithm, which is also reliable to surface with base point.