Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices
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 realiz...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/10/2254 |
| _version_ | 1827740855915511808 |
|---|---|
| author | Wenlong Zeng Jianzhou Liu Hongmin Mo |
| author_facet | Wenlong Zeng Jianzhou Liu Hongmin Mo |
| author_sort | Wenlong Zeng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T03:32:17Z |
| format | Article |
| id | doaj.art-5f206d2a9ad243b5af2a862fa30f008a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:32:17Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5f206d2a9ad243b5af2a862fa30f008a2023-11-18T02:18:15ZengMDPI AGMathematics2227-73902023-05-011110225410.3390/math11102254Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type MatricesWenlong Zeng0Jianzhou Liu1Hongmin Mo2Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaKey Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaCollege of Mathematics and Statistics, Jishou University, Jishou 416099, ChinaIt 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.https://www.mdpi.com/2227-7390/11/10/2254Dashnic–Zusmanovich-type matricesinfinity norm boundSchur complementscaling matrixsmallest singular value |
| spellingShingle | Wenlong Zeng Jianzhou Liu Hongmin Mo Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices Mathematics Dashnic–Zusmanovich-type matrices infinity norm bound Schur complement scaling matrix smallest singular value |
| title | Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices |
| title_full | Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices |
| title_fullStr | Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices |
| title_full_unstemmed | Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices |
| title_short | Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices |
| title_sort | schur complement based infinity norm bound for the inverse of dashnic zusmanovich type matrices |
| topic | Dashnic–Zusmanovich-type matrices infinity norm bound Schur complement scaling matrix smallest singular value |
| url | https://www.mdpi.com/2227-7390/11/10/2254 |
| work_keys_str_mv | AT wenlongzeng schurcomplementbasedinfinitynormboundfortheinverseofdashniczusmanovichtypematrices AT jianzhouliu schurcomplementbasedinfinitynormboundfortheinverseofdashniczusmanovichtypematrices AT hongminmo schurcomplementbasedinfinitynormboundfortheinverseofdashniczusmanovichtypematrices |