thiele takes as the first argument a matrix data of type n× 2 where that i -th row holds coordinates x and y of i -th point, respectively. The second argument is v, which may be an identifier, number or any symbolic expression. Function returns R(v) where R is the rational interpolant. Instead of a single matrix data, two vectors x=(x1,x2,…,xn) and y=(y1,y2,…,yn) may be given (in this case, v is given as the third argument).
This method computes Thiele interpolated continued fraction based on the concept of reciprocal differences.
It is not guaranteed that R is continuous, i.e. it may have singularities in the shortest segment which contains all components of x .
In the following example, data is obtained by sampling the function f(x)=(1−x4) e1−x3 .