@article{a2df5a76317740229204218e1ef1e8d2, title = "A fast algorithm for scalar Nevanlinna-Pick interpolation", abstract = "In this paper, we derive a fast algorithm for the scalar Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk |z|i satisfying the Pick condition for 1≦i≦n, the new Nevanlinna-Pick interpolation algorithm requires only O(n) arithmetic operations to evaluate the interpolatory rational function at a particular value of z, in contrast to the classical algorithm which requires O(n2) arithmetic operations to compute the so-called Fenyves array (which is inherent in the classical algorithm). The new algorithm bypasses the generation of the Fenyves array to speed up the computation, and also yields a parallel scheme requiring only O(log n) arithmetic operations on a concurrent-read, exclusive-write parallel random access machine with n processors. We must remark that the rational function f(z) computed by the new algorithm is one degree higher than the function computed by the classical algorithm. {\textcopyright} 1993 Springer-Verlag.", keywords = "Mathematics Subject Classification (1991): 65D05, 68Q25, 93B40", author = "{Kaya Koc}, Cetin and Guanrong Chen", year = "1993", month = dec, doi = "10.1007/BF01388683", language = "English", volume = "64", pages = "115--126", journal = "Numerische Mathematik", issn = "0029-599X", publisher = "Springer", number = "1", }