TY - JOUR
T1 - A fast algorithm for scalar Nevanlinna-Pick interpolation
AU - Kaya Koc, Cetin
AU - Chen, Guanrong
PY - 1993/12
Y1 - 1993/12
N2 - 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. © 1993 Springer-Verlag.
AB - 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. © 1993 Springer-Verlag.
KW - Mathematics Subject Classification (1991): 65D05, 68Q25, 93B40
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U2 - 10.1007/BF01388683
DO - 10.1007/BF01388683
M3 - 21_Publication in refereed journal
VL - 64
SP - 115
EP - 126
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1
ER -