Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices

Wenlong Zeng, Jianzhou Liu () and Hongmin Mo
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Wenlong Zeng: Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Jianzhou Liu: Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Hongmin Mo: College of Mathematics and Statistics, Jishou University, Jishou 416099, China

Mathematics, 2023, vol. 11, issue 10, 1-12

Abstract: It is necessary to explore more accurate estimates of the infinity norm of the inverse of a matrix in both theoretical analysis and practical applications. This paper focuses on obtaining a tighter upper bound on the infinite norm of the inverse of Dashnic–Zusmanovich-type (DZT) matrices. The realization of this goal benefits from constructing the scaling matrix of DZT matrices and the diagonal dominant degrees of Schur complements of DZT matrices. The effectiveness and superiority of the obtained bounds are demonstrated through several numerical examples involving random variables. Moreover, a lower bound for the smallest singular value is given by using the proposed bound.

Keywords: Dashnic–Zusmanovich-type matrices; infinity norm bound; Schur complement; scaling matrix; smallest singular value (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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