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A NON-RECURSIVE APPROACH TO NEVANLINNA-PICK INTERPOLATION PROBLEM

  • Kim, Jeongook (Department of Mathematics, Chonnam National University)
  • Received : 2019.07.23
  • Accepted : 2019.10.11
  • Published : 2019.12.25

Abstract

A solution for Nevanlinna-Pick interpolation problem with low complexity is constructed via non-recursive method. More precisely, a stable rational function satifying the given interpolation data in the complex right half plane is found by solving a homogeneous interpolation problem related to a minial interpolation problem for the given data in the right half plane together with its mirror-image data.

Keywords

References

  1. Antoulas, A.C., Anderson, B.D.O., On the scalar rational interpolation problem, IMA J. Math. Control Inform. 3:61-88, 1986. https://doi.org/10.1093/imamci/3.2-3.61
  2. Antoulas, A.C., Anderson, B.D.O. On the problem of stable rational interpolation, Linear Alg. & Appl., 122/123, 301-328, 1989. https://doi.org/10.1016/0024-3795(89)90657-5
  3. Antouals, A.C., Ball, J.A., Kang(Kim), J., Willems, J.C., On the solution of minimal rational interpolation problem, Lin. Alg.& Appl., 137/138, 511-573, 1990. https://doi.org/10.1016/0024-3795(90)90141-X
  4. Ball, J.A., Gohberg, I., Rodman, L., Interpolation of Rational Matrix Functions, monograph, Birkhauser, OT 45, Basel, 1990.
  5. Ball,J., Kim,J., Stability and McMillan degree for rational matrix interpolants, Lin. Alg. & Appl., 196, 207-232, 1994. https://doi.org/10.1016/0024-3795(94)90325-5
  6. Belevitch, V., Interpolation matrices, Philips Res. Repts 25, 337-369, 1970.
  7. Donoghue, Jr., W.F., Monotone Matrix Functions and Analytic Continuation, monograph, Springer-Verlag, New York, 1974
  8. Kailath, T : Linear Systems, monograph, Prentice-Hall, 1980.
  9. Kim, J.:A tangential interpolation problem for rational matrix functions from a classical point of view, Honam Math. Journal, 39(4), 617-635, 2017. https://doi.org/10.5831/HMJ.2017.39.4.617
  10. Nevanlinna, R. : Uber beschrankte analytische Funktionen, Ann. Acad. Sci. Fenn. Ser. A, 32(7), 1-75, 1929.