Relevant bibliographies by topics / Pick–Nevanlinna interpolation Problem

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Academic literature on the topic 'Pick–Nevanlinna interpolation Problem'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Pick–Nevanlinna interpolation Problem"

1

Yücesoy, Veysel, та Hitay Özbay. "On the real, rational, bounded, unit interpolation problem in ℋ∞ and its applications to strong stabilization". Transactions of the Institute of Measurement and Control 41, № 2 (2018): 476–83. http://dx.doi.org/10.1177/0142331218759598.

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One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in [Formula: see text] satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.
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2

Fisher, Stephen D., and Dmitry Khavinson. "Extreme Pick-Nevanlinna Interpolants." Canadian Journal of Mathematics 51, no. 5 (1999): 977–95. http://dx.doi.org/10.4153/cjm-1999-043-5.

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AbstractFollowing the investigations of B. Abrahamse [1], F. Forelli [11], M. Heins [14] and others, we continue the study of the Pick-Nevanlinna interpolation problem inmultiply-connected planar domains. One major focus is on the problem of characterizing the extreme points of the convex set of interpolants of a fixed data set. Several other related problems are discussed.
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3

Davidson, Kenneth R., Vern I. Paulsen, Mrinal Raghupathi, and Dinesh Singh. "A constrained Nevanlinna-Pick interpolation problem." Indiana University Mathematics Journal 58, no. 2 (2009): 709–32. http://dx.doi.org/10.1512/iumj.2009.58.3486.

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4

Takahashi, Sechiko. "A sufficient condition for Nevanlinna parametrization and an extension of Heins theorem." Nagoya Mathematical Journal 153 (1999): 87–100. http://dx.doi.org/10.1017/s0027763000006905.

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AbstractAn extended interpolation problem on a Riemann surface is formulated in terms of local rings and ideals. A sufficient condition for Nevanlinna parametrization is obtained. By means of this, Heins theorem on Pick-Nevanlinna interpolation in doubly connected domains is generalized to extended interpolation.
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5

Derkach, V. A. "On Schur–Nevanlinna–Pick Indefinite Interpolation Problem." Ukrainian Mathematical Journal 55, no. 10 (2003): 1567–87. http://dx.doi.org/10.1023/b:ukma.0000022069.69507.bc.

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6

Kosiński, Łukasz, and Włodzimierz Zwonek. "Nevanlinna-Pick interpolation problem in the ball." Transactions of the American Mathematical Society 370, no. 6 (2017): 3931–47. http://dx.doi.org/10.1090/tran/7063.

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7

Agler, Jim, and John E. MCarthy. "Nevanlinna-Pick interpolation on the bidisk." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 506 (1999): 191–204. http://dx.doi.org/10.1515/crll.1999.506.191.

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Abstract We solve the matrix-valued Nevanlinna-Pick problem in the space of bounded analytic functions on the bidisk, and give a description of all the interpolating functions. We also prove the Toeplitz-corona theorem on the bidisk.
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8

Saitoh, Saburou. "A counter example in the Pick-Nevanlinna interpolation problem." Archiv der Mathematik 51, no. 2 (1988): 164–65. http://dx.doi.org/10.1007/bf01206474.

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9

Luxemburg, Leon A., and Philip R. Brown. "The scalar Nevanlinna–Pick interpolation problem with boundary conditions." Journal of Computational and Applied Mathematics 235, no. 8 (2011): 2615–25. http://dx.doi.org/10.1016/j.cam.2010.11.013.

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10

Oloomi, H. M. "Nevanlinna-Pick interpolation problem for two frequency scale systems." IEEE Transactions on Automatic Control 40, no. 1 (1995): 169–73. http://dx.doi.org/10.1109/9.362876.

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