Geodesic
Implicit iterative algorithm for solving regularized total~least squares problems
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 311-321

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

The article considers a new iterative algorithm for solving total least squares problems. A new version of the implicit method of simple iterations based on singular value decomposition is proposed for solving a biased normal system of algebraic equations. The use of the implicit method of simple iterations based on singular value decomposition makes it possible to replace an ill-conditioned problem with a sequence of problems with a smaller condition number. This makes it possible to significantly increase the computational stability of the algorithm and, at the same time, ensures its high rate of convergence. Test examples shown that the proposed algorithm has a higher accuracy compared to the solutions obtained by non-regularized total least squares algorithms, as well as the total least squares solution with Tikhonov regularization.
Keywords: implicit regularization, total least squares, ill-conditioning, iterative regularization methods.
Mots-clés : singular value decomposition 
@article{VSGTU_2022_26_2_a5,
     author = {D. V. Ivanov and A. I. Zhdanov},
     title = {Implicit iterative algorithm for solving regularized total~least squares problems},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {311--321},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a5/}
}
TY  - JOUR
AU  - D. V. Ivanov
AU  - A. I. Zhdanov
TI  - Implicit iterative algorithm for solving regularized total~least squares problems
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2022
SP  - 311
EP  - 321
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a5/
LA  - en
ID  - VSGTU_2022_26_2_a5
ER  - 
%0 Journal Article
%A D. V. Ivanov
%A A. I. Zhdanov
%T Implicit iterative algorithm for solving regularized total~least squares problems
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2022
%P 311-321
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a5/
%G en
%F VSGTU_2022_26_2_a5
D. V. Ivanov; A. I. Zhdanov. Implicit iterative algorithm for solving regularized total~least squares problems. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 311-321. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a5/