Geodesic
On convergence of the inverse iteration algorithm for modified Prony method
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1513-1529.

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

In the nonlinear eigenvalue problem of modified Prony method under small perturbations the global convergence of first inverse iteration algorithm of M. Osborne (1970) is investigated.
Keywords: difference equations, parameter identification, modified Prony method, nonlinear eigenvalue problem, inverse iteration
Mots-clés : global convergence. 
@article{SEMR_2018_15_a116,
     author = {A. A. Lomov},
     title = {On convergence of the inverse iteration algorithm for modified {Prony} method},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1513--1529},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a116/}
}
TY  - JOUR
AU  - A. A. Lomov
TI  - On convergence of the inverse iteration algorithm for modified Prony method
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1513
EP  - 1529
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a116/
LA  - ru
ID  - SEMR_2018_15_a116
ER  - 
%0 Journal Article
%A A. A. Lomov
%T On convergence of the inverse iteration algorithm for modified Prony method
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1513-1529
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a116/
%G ru
%F SEMR_2018_15_a116
A. A. Lomov. On convergence of the inverse iteration algorithm for modified Prony method. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1513-1529. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a116/

[1] de Prony, Baron Gaspard Riche, “Essai éxperimental et analytique: sur les lois de la dilatabilité de fluides élastique et sur celles de la force expansive de la vapeur de l'alkool, à différentes températures”, Journal de l'École Polytechnique, 1 (1795), Cahier 22, 24–76

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

[3] Householder A. S., On Prony's method of fitting exponential decay curves and multiple-hit survival cerves, Report ORNL-455, Oak Ridge National Lab., Oak Ridge, Tennessee, 1950 | MR

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

[5] Peter T., Generalized Prony Method, Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades, Göttingen, 2013

[6] Roy R., Kailath T., “ESPRIT — Estimation of Signal Parameters via Rotational Invariance Techniques”, IEEE Transactions on Acoustics Speech and Signal Processing, 37:7 (1989), 984–995 | DOI

[7] Potts D., Tasche M., “Parameter estimation for nonincreasing exponential sums by Prony-like methods”, Linear Algebra and its Applications, 439:4 (2013), 1024–1039 | DOI | MR | Zbl

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

[9] Petersson J., 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

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

[11] Osborne M. R., “Some special nonlinear least squares problems”, SIAM J. Numer. Anal., 12:4 (1975), 571–592 | DOI | MR | Zbl

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

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

[14] Osborne M. R., Smyth G. K., “A modified Prony algorithm for fitting functions defined by difference equations”, SIAM J. Sci. Statist. Comput., 12:2 (1991), 362–382 | DOI | MR | Zbl

[15] Lomov A. A., “On asymptotic optimality of the orthoregressional estimators”, Journal of Applied and Industrial Mathematics, 10:4 (2016), 511–519 | DOI | MR | Zbl

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

[17] Osborne M. R., Smyth G. K., “A Modified Prony Algorithm for Exponential Function Fitting”, SIAM Journal of Scientific Computing, 16:1 (1995), 119–138 | DOI | MR | Zbl

[18] Wilkinson J. H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965 | MR | Zbl