The Schur complement of SDD$ _1 $ matrices and its applications

Shiyun Wang; Yun Li; Wanfu Tian; Shiyun Wang; Yun Li; Wanfu Tian

doi:10.3934/math.20251052

AIMS Mathematics

2025, Volume 10, Issue 10: 23676-23696. doi: 10.3934/math.20251052

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Research article

The Schur complement of SDD$ _1 $ matrices and its applications

College of Science, Shenyang Aerospace University, Shenyang, Liaoning, 110136, China

Received: 05 August 2025 Revised: 18 September 2025 Accepted: 25 September 2025 Published: 17 October 2025
MSC : 15A45, 15A48

The Schur complements of H-matrices have a wide range of practical applications. This paper explores the diagonally dominant degrees of the Schur complements of SDD$ _1 $ matrices and its applications. it concludes that the Schur complements can be also SDD$ _1 $ matrices under certain conditions. Moreover, the upper and lower bounds for the determinants of SDD$ _1 $ matrices are presented, and large-scale linear equations with the coefficient matrix being an SDD$ _1 $ matrix are solved by Schur-based methods. The numerical results are reported.
- SDD$ _1 $ matrix,
- Schur complement,
- diagonal-Schur complement,
- determinant,
- large scale linear equations,
- Schur-based method
Citation: Shiyun Wang, Yun Li, Wanfu Tian. The Schur complement of SDD$ _1 $ matrices and its applications[J]. AIMS Mathematics, 2025, 10(10): 23676-23696. doi: 10.3934/math.20251052

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Abstract

The Schur complements of H-matrices have a wide range of practical applications. This paper explores the diagonally dominant degrees of the Schur complements of SDD$ _1 $ matrices and its applications. it concludes that the Schur complements can be also SDD$ _1 $ matrices under certain conditions. Moreover, the upper and lower bounds for the determinants of SDD$ _1 $ matrices are presented, and large-scale linear equations with the coefficient matrix being an SDD$ _1 $ matrix are solved by Schur-based methods. The numerical results are reported.

References

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