On diagonal-Schur complements of block diagonally dominant matrices

Yao tang Li; Shun ping Ouyang; Shu juan Cao; Rui Wu Wang

doi:10.1016/j.amc.2010.02.038

On diagonal-Schur complements of block diagonally dominant matrices

Yao tang Li, Shun ping Ouyang, Shu juan Cao, Rui Wu Wang

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices.

Original language	English
Pages (from-to)	1383-1392
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	216
Issue number	5
DOIs	https://doi.org/10.1016/j.amc.2010.02.038
State	Published - 1 May 2010
Externally published	Yes

Keywords

Block strictly diagonally dominant matrix
Diagonal-Schur complement
Generalized block strictly diagonally dominant matrix
H-matrix
Schur complement

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title = "On diagonal-Schur complements of block diagonally dominant matrices",

abstract = "It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices.",

keywords = "Block strictly diagonally dominant matrix, Diagonal-Schur complement, Generalized block strictly diagonally dominant matrix, H-matrix, Schur complement",

author = "Li, {Yao tang} and Ouyang, {Shun ping} and Cao, {Shu juan} and Wang, {Rui Wu}",

year = "2010",

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doi = "10.1016/j.amc.2010.02.038",

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T1 - On diagonal-Schur complements of block diagonally dominant matrices

AU - Li, Yao tang

AU - Ouyang, Shun ping

AU - Cao, Shu juan

AU - Wang, Rui Wu

PY - 2010/5/1

Y1 - 2010/5/1

N2 - It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices.

AB - It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices.

KW - Block strictly diagonally dominant matrix

KW - Diagonal-Schur complement

KW - Generalized block strictly diagonally dominant matrix

KW - H-matrix

KW - Schur complement

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DO - 10.1016/j.amc.2010.02.038

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VL - 216

SP - 1383

EP - 1392

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 5

ER -

On diagonal-Schur complements of block diagonally dominant matrices

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