![]() |
![]() |
ETNA - Electronic Transactions on Numerical Analysis
|
![]() |
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
![]() |
|
DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
|
ETNA - Electronic Transactions on Numerical Analysis, pp. 244-270, 2023/03/06
Cvetković-Kostić-Varga (CKV)-type matrices play a significant role in numerical linear algebra. However, verifying whether a given matrix is a CKV-type matrix is complicated because it involves choosing a suitable subset of $\{1,2,\ldots,n\}$. In this paper, we give some easily computable and verifiable equivalent conditions for a CKV-type matrix, and based on these conditions, two direct algorithms with less computational cost for identifying CKV-type matrices are put forward. Moreover, by considering the matrix sparsity pattern, two classes of matrices called $S$-Sparse Ostrowski-Brauer type-I and type-II matrices are proposed and then proved to be subclasses of CKV-type matrices. The relationships with other subclasses of $H$-matrices are also discussed. Besides, a new eigenvalue localization set involving the sparsity pattern for matrices is presented, which requires less computational cost than that provided by Cvetković et al. [Linear Algebra Appl., 608 (2021), pp.158–184].
Keywords: CKV-type matrices, S-Sparse Ostrowski-Brauer type-I matrices, S-Sparse Ostrowski-Brauer type-II matrices, H-matrices