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M. N. Zav'yalov, L. S. Maergoiz

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

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

C_k := Y(t_k ), t_k = t ₀ + kd, d > 0, k = 0, 1, … , N, N ≥ n.

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).

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 12, 10/2004
Pages: 435 - 446

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