On Cvetković-Kostić-Varga type matrices

Abstract

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, . . . , 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].