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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 12, Issue 4 (Oct 2004)


Operator of extrapolation from a finite set of quasi-polynomial vector-functions and its applications

M. N. Zav'yalov / L. S. Maergoiz
  • Krasnoyarsk State Academy of Architecture and Civil Engineering. Svobodny prosp., 82, Krasnoyarsk, 660041, Russia. E-mail:

We consider the inverse problem for a first-order homogeneous system of linear ordinary differential equations (LODE),

where Y(t) is a vector-function with n components and A is an unknown matrix of dimensionality n × n with constant complex coefficients and certain restrictions imposed on its eigenvalues.

The boundary conditions are

Ck := Y(tk ), tk = t 0 + kd, d > 0, k = 0, 1, … , N, Nn.

Here is a given system of vectors in .

This problem is equivalent to the problem of extrapolating a vector-function composed of quasi-polynomials representing solutions of some LODEs with constant coefficients of order n.

The zone of solution stability of the system against small-amplitude input data oscillations is described. The results obtained are used to construct an approximation algorithm for a real vector-function of one variable set at a finite number of nodes of a uniform grid (modified Prony algorithm).

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Published Online:

Published in Print: 2004-10-01

Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/1569394042248256.

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