On Schur complements of Dashnic–Zusmanovich type matrices

ABSTRACT

It is shown in this paper that the Schur complements and the diagonal-Schur complements of DZ-type matrices are DZ-type matrices under some conditions. A numerical example for solving the linear equations with the coefficient matrix being a DZ-type matrix is given to show that the Schur-based Gauss–Seidel iteration method and the Schur-based conjugate gradient method can compute out the solution faster.

Keywords:

• Dashnic–Zusmanovich type matrices
• H-matrices
• Schur complements
• diagonal-Schur complements
• diagonally dominant degree

AMS Subject Classifications:

• 15A45
• 15A48

Acknowledgments

The authors are grateful to the anonymous referees and Handling Editor Professor Rajesh Pereira for their more than one hundred constructive comments and suggestions, which greatly improve our manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 12061087]; the Applied Basic Research Programs of Science and Technology Department of Yunnan Province [grant number 2018FB001]; Program for Excellent Young Talents, Yunnan University; Yunnan Provincial Ten Thousands Plan Young Top Talents; and Natural Science Foundation of Guizhou Minzu University [grant number GZMU[2019]YB09].