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Applied Mathematics and ComputationVolume 208, Issue 1, 1 February 2009, Pages 225-230

Special H-matrices and their Schur and diagonal-Schur complements(Article)

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  • aFaculty of Science, Mathematics and Informatics, University of Novi Sad, Trg D. Obradovica 4, Novi Sad, 21000, Serbia
  • bFaculty of Technical Sciences, University of Novi Sad, Serbia

Abstract

It is well known, see [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246-251 [2]; J. Liu, J. Li, Z. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Alg. Appl. 428 (2008) 1009-1030] [14], that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant, as well as its diagonal-Schur complement. Also, if a matrix is an H-matrix, then its Schur complement and diagonal-Schur complement are H-matrices, too, see [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Alg. Appl. 389 (2004) 365-380] [13]. Recent research, see [J. Liu, Y. Huang, F. Zhang, The Schur complements of generalized doubly diagonally dominant matrices, Linear Alg. Appl. 378 (2004) 231-244 [12]; J. Liu, J. Li, Z. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Alg. Appl. 428 (2008) 1009-1030] [14], showed that the similar statements hold for some special subclasses of H-matrices. The aim of this paper is to give more invariance results of this type, and simplified proofs for some already known results, by using scaling approach. © 2008 Elsevier Inc. All rights reserved.

Author keywords

Diagonal scalingH-matricesSchur complement

Indexed keywords

Engineering uncontrolled terms:CarlsonDiagonal scalingH-matricesMarkham (CO)Schur complement

Funding details

Funding sponsor Funding number Acronym
Provincial Secretariat for Science and Technological Development0708PSSTD
Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja144025MPNTR

  • 1

    This work is partly supported by the Ministry of Science of Serbia, grant 144025 and by the Provincial Secretariat of Science and Technological Development of Vojvodina, grant 0708.

  • ISSN: 00963003
  • CODEN: AMHCB
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.amc.2008.11.040
  • Document Type: Article

  Cvetković, L.; Faculty of Science, Mathematics and Informatics, University of Novi Sad, Trg D. Obradovica 4, Serbia;
© Copyright 2009 Elsevier B.V., All rights reserved.

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