Geodesic
A least squares method for sums of functions satisfying the differential
Numerical methods and programming, Tome 4 (2003) no. 1, pp. 167-171

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

We propose a linear algorithm for determining the parameters of two functions on the basis of their linear combination. These functions must satisfy first-order differential equations with polynomial coefficients, whereas the parameters to be found are the coefficients of these polynomials. The algorithm is based on the least squares method and consists of sequential solution of the following two linear problems: determining the coefficients of polynomial terms in the differential equation satisfied by a linear combination of two given functions and determining the function parameters with the use of these polynomial coefficients. Numerical results obtained according to the above scheme confirm good performance of our method under weak normal noise (with dispersion less than 3 per cent)
Keywords: least squares method, differential equations, linearity, noisy systems. 
@article{VMP_2003_4_1_a15,
     author = {O. I. Berngardt and A. L. Voronov},
     title = {A least squares method for sums of functions satisfying the differential},
     journal = {Numerical methods and programming},
     pages = {167--171},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2003_4_1_a15/}
}
TY  - JOUR
AU  - O. I. Berngardt
AU  - A. L. Voronov
TI  - A least squares method for sums of functions satisfying the differential
JO  - Numerical methods and programming
PY  - 2003
SP  - 167
EP  - 171
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2003_4_1_a15/
LA  - ru
ID  - VMP_2003_4_1_a15
ER  - 
%0 Journal Article
%A O. I. Berngardt
%A A. L. Voronov
%T A least squares method for sums of functions satisfying the differential
%J Numerical methods and programming
%D 2003
%P 167-171
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2003_4_1_a15/
%G ru
%F VMP_2003_4_1_a15
O. I. Berngardt; A. L. Voronov. A least squares method for sums of functions satisfying the differential. Numerical methods and programming, Tome 4 (2003) no. 1, pp. 167-171. http://geodesic.mathdoc.fr/item/VMP_2003_4_1_a15/