On convergence of M.~Osborne' inverse iteration algorithms for modified Prony method
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1916-1926.

Voir la notice de l'article provenant de la source Math-Net.Ru

A convergence of two inverse iteration algorithms of M. Osborne in the nonlinear eigenvalue problem of modified Prony method under small perturbations is investigated.
Keywords: difference equations, parameter identification, modified Prony method, nonlinear eigenvalue problem, inverse iteration
Mots-clés : semilocal convergence.
@article{SEMR_2019_16_a121,
     author = {A. A. Lomov},
     title = {On convergence of {M.~Osborne'} inverse iteration algorithms for modified {Prony} method},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1916--1926},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a121/}
}
TY  - JOUR
AU  - A. A. Lomov
TI  - On convergence of M.~Osborne' inverse iteration algorithms for modified Prony method
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1916
EP  - 1926
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a121/
LA  - ru
ID  - SEMR_2019_16_a121
ER  - 
%0 Journal Article
%A A. A. Lomov
%T On convergence of M.~Osborne' inverse iteration algorithms for modified Prony method
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1916-1926
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a121/
%G ru
%F SEMR_2019_16_a121
A. A. Lomov. On convergence of M.~Osborne' inverse iteration algorithms for modified Prony method. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1916-1926. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a121/

[1] M. R. Osborne, G. K. Smyth, “A modified Prony algorithm for fitting functions defined by difference equations”, SIAM J. Sci. Statist. Comput., 12 (1991), 362–382 | DOI | MR | Zbl

[2] M. R. Osborne, G. K. Smyth, “A Modified Prony Algorithm for Exponential Function Fitting”, SIAM Journal of Scientific Computing, 16 (1995), 119–138 | DOI | MR | Zbl

[3] V. Pereyra, G. Scherer, “Exponential data fitting”, Exponential Data Fitting and Its Applications, Bentham Science Publishers, 2010, 1–26

[4] A. A. Lomov, “On convergence of the inverse iteration algorithm for modified Prony method”, SEMR, 15 (2018), 1513–1529 | MR | Zbl

[5] V. I. Kostin, “On extremum points of some function”, Upravlyaemye sistemy, 24, Institute of Mathematics of SB AS USSR, Novosibirsk, 1984, 35–42 (in Russian) | MR

[6] J. Petersson, Holmström K., “A review of the parameter estimation problem of fitting positive exponential sums to empirical data”, Applied Mathematics and Computation, 126:1 (2002), 31–61 | DOI | MR | Zbl

[7] B. Moor De, “Structured total least squares and $L_{2}$ approximation problems”, Linear Algebra Appl., 188–189 (1993), 163–207 | DOI | MR | Zbl

[8] M. R. Osborne, “Some special nonlinear least squares problems”, SIAM J. Numer. Anal., 12 (1975), 571–592 | DOI | MR | Zbl

[9] M. R. Osborne, “A class of nonlinear regression problems”, Data Representation, University of Queensland Press, St. Lucia, 1970, 94–101 | Zbl

[10] A. O. Egorshin, V. P. Budyanov, “Smoothing of signals and estimation of dynamic parameters in automatic systems using a digital computer”, Avtometriya, 1 (1973), 78–82 (in Russian)

[11] A. O. Egorshin, “Least squares method and the fast algorithms in variational problems of identification and filtration (VI method)”, Avtometriya, 1 (1988), 30–42 (in Russian)

[12] Journal of Mathematical Sciences, 195 (2013), 791–804 | DOI | MR | Zbl

[13] Journal of Mathematical Sciences, 188:4 (2013), 410–434 | DOI | MR | Zbl

[14] S. L. Marple, Digital spectral analysis with applications, Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1986 | MR