Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points

Bivariate Blending Thiele-Werner’s Osculatory Rational Interpolation

Continued Fractions with Three Limit Points

The research described in this paper was motivated by an enigmatic entry in Ramanujan’s lost notebook [11, p. 45] in which he claimed, in an unorthodox fashion, that a certain q-continued fraction possesses three limit points. More precisely, he claimed that as n tends to ∞ in the three residue classes modulo 3, the nth partial quotients tend, respectively, to three distinct limits, which he ex...

A weighted bivariate blending rational interpolation based on function values

This paper presents a new weighted bivariate blending rational spline interpolation based on function values. This spline interpolation has the following advantages: firstly, it can modify the shape of the interpolating surface by changing the parameters under the condition that the values of the interpolating nodes are fixed; secondly, the interpolating function is C-continuous for any positiv...

Homogeneous Interpolation and Some Continued Fractions

We prove: if d/m < 2280/721, there is no curve of degree d passing through n = 10 general points with multiplicity m in P. Similar results are given for other special values of n. Our bounds can be naturally written as certain palindromic continued fractions.

Orthogonal Rational Functions and Continued Fractions