Abstract
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 arithmetic operations only. There exist rational methods designed for checking the congruence of particular classes of unitoid matrices, for example, Hermitian, accretive, or dissipative matrices. We propose a rational algorithm for checking the congruence of general unitoid matrices. The algorithm is heuristic in the sense that the user is required to set 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 being checked.
Similar content being viewed by others
REFERENCES
Johnson, C.R. and Furtado, S., A Generalization of Sylvester’s Law of Inertia, Lin. Alg. Appl., 2001, vol. 338, pp. 287–290.
Ikramov, Kh.D., On the Congruent Selection of Jordan Blocks from a Singular Square Matrix, Sib. Zh. Vych. Mat., 2018, vol. 21, no. 3, pp. 255–258.
Ikramov, Kh.D., Finite Spectral Procedures in Linear Algebra,Programmir., 1994, no. 1, pp. 56–69.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2021, Vol. 24, No. 2, pp. 166–177.https://doi.org/10.15372/SJNM20210204.
Rights and permissions
About this article
Cite this article
Ikramov, K.D., Nazari, A.M. A Rational Algorithm for Checking the Congruence of Unitoid Matrices. Numer. Analys. Appl. 14, 145–154 (2021). https://doi.org/10.1134/S199542392102004
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S199542392102004