ISSN:
0945-3245
Keywords:
65D05
;
68Q25
;
93B40
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In this paper, we derive a fast algorithm for the scalar Nevanlinna-Pick interpolation. Givenn distinct pointsz i in the unit disk |z|〈1 andn complex numbersw i satisfying the Pick condition for 1≦i≦n, the new Nevanlinna-Pick interpolation algorithm requires onlyO(n) arithmetic operations to evaluate the interpolatory rational function at a particular value ofz, in contrast to the classical algorithm which requiresO(n 2) 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 onlyO(logn) arithmetic operations on a concurrent-read, exclusive-write parallel random access machine withn processors. We must remark that the rational functionf(z) computed by the new algorithm is one degree higher than the function computed by the classical algorithm.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01388683
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