Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników


2015 | 13 | 1 |

Tytuł artykułu

An extended Prony’s interpolation scheme on an equispaced grid

Treść / Zawartość

Warianty tytułu

Języki publikacji



An interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension of the Prony method and can be useful for describing noisy and defected signals.








Opis fizyczny




  • Department of Applied Mathematics, Kaunas University of Technology, Studentu 50-325,
    LT-51368, Kaunas, Lithuania
  • Department of Applied Mathematics, Kaunas University of Technology, Studentu 50-325,
    LT-51368, Kaunas, Lithuania
  • Department of Mathematical Modelling, Vilnius Gediminas Technical University, Sauletekio 11, LT-10223, Vilnius,
  • Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of
    Technology, Studentu 50-147, LT-51368, Kaunas, Lithuania


  • [1] Badeau R., David B., High-resolution spectral analysis of mixtures of complex exponentials modulated by polynomials, IEEE Trans. Signal Process., 2006, 54, 1341–1350. [Crossref]
  • [2] Badeau R., Richard G., David B., Performance of ESPRIT for estimating mixtures of complex exponentials modulated by polynomials, IEEE Trans. Signal Process., 2008, 56, 492–504. [WoS][Crossref]
  • [3] Ehlich H., Zeller K., Auswertung der Normen von Interpolationsoperatoren, Math. Ann., 1996, 164, 105–112. [Crossref]
  • [4] Higham N.J., The numerical stability of barycentric Lagrange interpolation, IMA J. Numer. Anal., 2004, 24, 547–556. [Crossref]
  • [5] Navickas Z., Bikulciene L., Expressions of solutions of ordinary differential equations by standard functions, Mathematical Modeling and Analysis, 2006, 11, 399–412.
  • [6] Peter T., Plonaka G., A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators, Inverse Problems, 2013, 29, 025001. [Crossref][WoS]
  • [7] Platte R.B., Trefethen L.N., Kuijlaars A.B.J., Impossibility of fast stable approximation of analytic functions from equispaced samples, SIAM Review, 2011, 53, 308–314. [WoS][Crossref]
  • [8] Ragulskis M., Lukoseviciute K., Navickas Z., Palivonaite R., Short-term time series forecasting based on the identification of skeleton algebraic sequences, Neurocomputing, 2011, 64, 1735–1747. [WoS][Crossref]
  • [9] Runge C., Uber empirische Funktionen and die Interpolation zwischen aquidistanten Ordinaten, Z. Math. Phys., 1901, 46 224– 243.
  • [10] Salzer H.E., Lagrangian interpolation at the Chebyshev points xn;υ = cos(υπ/n), υ = 0(1)n; some unnoted advantages, Computer J., 1972, 15, 156–159.
  • [11] Schonhage A., Fehlerfortpflanzung bei Interpolation, Numer. Math., 1961, 3, 62–71. [Crossref]
  • [12] Trefethen L.N., Pachon R., Platte R.B., Driscoll T.A., Chebfun Version 2,, Oxford University, 2008.
  • [13] Turetskii A.H., The bounding of polynomials prescribed at equally distributed points, Proc. Pedag. Inst. CityplaceVitebsk, 1940, 3, 117–127.
  • [14] Osborne M.R., Smyth G.K., A Modified Prony Algorithm For Exponential Function Fitting, SIAM Journal of Scientific Computing, 1995, 16, 119–138.
  • [15] Martin C., Miller J., Pearce K., Numerical solution of positive sum exponential equations, Applied Mathematics and Computation, 1989, 34, 89–93.
  • [16] Fuite J., Marsh R.E., Tuszynski J.A., An application of Prony’s sum of exponentials method to pharmacokinetic data analysis, Commun. Comput. Phys., 2007, 2, 87–98.
  • [17] Giesbrecht M., Labahn G., Wen-shin Lee, Symbolic-numeric sparse interpolation of multivariate polynomials, Journal of Symbolic Computation, 2009, 44, 943–959.
  • [18] Steedly W., Ying C.J., Moses O.L., A modified TLS-Prony method using data decimation, IEEE Transactions on Signal Processing, 1992, 42, 2292–2303. [Crossref]
  • [19] Kurakin V.L., Kuzmin A.S., Mikhalev A.V., Nechavev A.A., Linear recurring sequneces over rings and modules, Journal of Mathematical Sciences, 1995, 76, 2793–2915.
  • [20] Kurakin V., Linear complexity of polinear sequences, Disctrete Math. Appl., 2001, 11, 1–51. [Crossref]
  • [21] Potts D., Tasche M., Parameter estimation for multivariate exponential sums, Electron. Trans. Numer. Anal., 2013, 40, 204–224.
  • [22] Kaltofen E., Villard G., On the complexity of computing determinants, Computers Mathematics Proc. Fifth Asian Symposium (ASCM 2001), Lecture Notes Series on Computing, 2001, 9, 13–27.
  • [23] Kaw A., Egwu K., Numerical Methods with Applications, Textbooks collection Book 11, 2010, ch. 5.

Typ dokumentu



Identyfikator YADDA

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.