Comments on "A Simple and Accurate Algorithm for Barycentric Rational Interpolation"

First, I would like to thank the author of ”Comments on ’A Simple and Accurate Algorithm for Barycentric Rational Interpolation’” (hereafter referred to as ”the comments”) for their interest in my work [1]. The author of the comments points out a novel relationship between barycentric rational interpolation, the Welch-Berlekamp key equation and Gröbner bases. This could turn out to be a very promising novel approach for fast barycentric interpolation, since as to this author’s knowledge, the results about barycentric interpolation available in the literature (see references [13-17] in [1]) never mention the potential link with the Welch-Berlekamp key equation and/or Gröbner bases. However, the results in [1] with respect to the null space of a certain Löwner matrix have not been invalidated by the comments. As a last remark, it should be noted that the null space of a matrix can be calculated by other means than the SVD, e.g. by the ’cheaper’ QR decomposition.