"Construction of rational interpolations using Mamquist-Takenaka systems"Pap, MargitRational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in the frequency (Laplace) domain. Using rational functions, the goal of this paper to compute models that match (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 using only N sampling nodes (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. The poster/talk is based on the results, published in the following paper NAGY-CSIHA, Z. and PAP, M., and WEISZ, F. (2023). Construction of rational interpolations using Mamquist-Takenaka systems. Constructive Mathematical Analysis, 6(1), 55-76. https://doi.org/10.33205/cma.1251068 |
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