Construction of rational interpolations using Mamquist-Takenaka systems

Authors : Zsuzsanna NAGYCSIHA, Margıt PAP, Ferenc WEİSZ

Pages : 55-76

Doi:10.33205/cma.1251068

View : 14 | Download : 11

Publication Date : 2023-03-15

Article Type : Research Paper

Abstract :Rational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in the frequency insert ignore into journalissuearticles values(Laplace); domain. Using rational functions, the goal of this paper to compute models that match insert ignore into journalissuearticles values(interpolate); given data sets of measurements. In this paper, the authors show that using special rational orthonormal systems, the Malmquist-Takenaka systems, it is possible to write the rational interpolant $r_{insert ignore into journalissuearticles values(n, m);}$, for $n=N-1, m=N$ using only $N$ sampling nodes insert ignore into journalissuearticles values(instead of $2N$ nodes); if the interpolating nodes are in the complex unit circle or on the upper half-plane. Moreover, the authors prove convergence results related to the rational interpolant. They give an efficient algorithm for the determination of the rational interpolant.
Keywords : Rational interpolation, Hardy spaces, Malmquist Takenaka systems, discrete biorthogonality