Inverse properties of a class of seven-diagonal (near) Toeplitz matrices
This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-10-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2021-0148 |
| _version_ | 1828190516009762816 |
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| author | Kurmanbek Bakytzhan Erlangga Yogi Amanbek Yerlan |
| author_facet | Kurmanbek Bakytzhan Erlangga Yogi Amanbek Yerlan |
| author_sort | Kurmanbek Bakytzhan |
| collection | DOAJ |
| description | This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method. |
| first_indexed | 2024-04-12T08:23:48Z |
| format | Article |
| id | doaj.art-ef8f13d8459b4e729cee1887269f0872 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-12T08:23:48Z |
| publishDate | 2021-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-ef8f13d8459b4e729cee1887269f08722022-12-22T03:40:28ZengDe GruyterSpecial Matrices2300-74512021-10-01101678610.1515/spma-2021-0148Inverse properties of a class of seven-diagonal (near) Toeplitz matricesKurmanbek Bakytzhan0Erlangga Yogi1Amanbek Yerlan2Nazarbayev University, Department of Mathematics, 53 Kabanbay Batyr Ave, Nur-Sultan 010000, KazakhstanZayed University, Department of Mathematics, Abu Dhabi Campus, P.O. Box 144534, United Arab EmiratesNazarbayev University, Department of Mathematics, 53 Kabanbay Batyr Ave, Nur-Sultan 010000, KazakhstanThis paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.https://doi.org/10.1515/spma-2021-0148seven-diagonal matricestoeplitzexact inverseupper bound of norm of inverse15a6015b0565l10 |
| spellingShingle | Kurmanbek Bakytzhan Erlangga Yogi Amanbek Yerlan Inverse properties of a class of seven-diagonal (near) Toeplitz matrices Special Matrices seven-diagonal matrices toeplitz exact inverse upper bound of norm of inverse 15a60 15b05 65l10 |
| title | Inverse properties of a class of seven-diagonal (near) Toeplitz matrices |
| title_full | Inverse properties of a class of seven-diagonal (near) Toeplitz matrices |
| title_fullStr | Inverse properties of a class of seven-diagonal (near) Toeplitz matrices |
| title_full_unstemmed | Inverse properties of a class of seven-diagonal (near) Toeplitz matrices |
| title_short | Inverse properties of a class of seven-diagonal (near) Toeplitz matrices |
| title_sort | inverse properties of a class of seven diagonal near toeplitz matrices |
| topic | seven-diagonal matrices toeplitz exact inverse upper bound of norm of inverse 15a60 15b05 65l10 |
| url | https://doi.org/10.1515/spma-2021-0148 |
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