Geodesic
A rational algorithm for checking the congruence of unitoid matrices
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 2, pp. 167-177

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

A matrix is said to be unitoid if it can be brought to diagonal form by a congruence transformation. We say that an algorithm is rational if it is finite and uses the arithmetic operations only. There exist rational methods designed for checking congruence of particular classes of unitoid matrices, for example, Hermitian, accretive, or dissipative matrices. We propose a rational algorithm for checking congruence of general unitoid matrices. The algorithm is heuristic in the sense that the user is required to set the values of two integral parameters $M$ and $N$. The choice of these values depends on the available a priori information about the proximity of neighboring canonical angles of the matrices under checking. 
@article{SJVM_2021_24_2_a3,
     author = {Kh. D. Ikramov and A. M. Nazari},
     title = {A rational algorithm for checking the congruence of unitoid matrices},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {167--177},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_2_a3/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
AU  - A. M. Nazari
TI  - A rational algorithm for checking the congruence of unitoid matrices
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2021
SP  - 167
EP  - 177
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2021_24_2_a3/
LA  - ru
ID  - SJVM_2021_24_2_a3
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%A A. M. Nazari
%T A rational algorithm for checking the congruence of unitoid matrices
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2021
%P 167-177
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2021_24_2_a3/
%G ru
%F SJVM_2021_24_2_a3
Kh. D. Ikramov; A. M. Nazari. A rational algorithm for checking the congruence of unitoid matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 2, pp. 167-177. http://geodesic.mathdoc.fr/item/SJVM_2021_24_2_a3/