A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices
As a generalization of k -tridiagonal matrices, many variations of ( p , q )-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n -square ( p , q )-tridiagonal matrices under a certain conditio...
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| Veröffentlicht in: | Numerical algorithms Jg. 93; H. 2; S. 899 - 917 |
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| Sprache: | Englisch |
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01.06.2023
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| ISSN: | 1017-1398, 1572-9265 |
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| Abstract | As a generalization of
k
-tridiagonal matrices, many variations of (
p
,
q
)-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of
n
-square (
p
,
q
)-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function. |
|---|---|
| AbstractList | As a generalization of k-tridiagonal matrices, many variations of (p,q)-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n-square (p,q)-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function. As a generalization of k -tridiagonal matrices, many variations of ( p , q )-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n -square ( p , q )-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function. |
| Author | Xie, Rong Xu, Xiao-Yan Jia, Ji-Teng Ni, Shuo Wang, Jie |
| Author_xml | – sequence: 1 givenname: Ji-Teng surname: Jia fullname: Jia, Ji-Teng email: lavenderjjt@163.com organization: School of Mathematics and Statistics, Xidian University – sequence: 2 givenname: Rong surname: Xie fullname: Xie, Rong organization: School of Mathematics and Statistics, Xidian University – sequence: 3 givenname: Xiao-Yan surname: Xu fullname: Xu, Xiao-Yan organization: School of Economics & Management, Xidian University – sequence: 4 givenname: Shuo surname: Ni fullname: Ni, Shuo organization: School of Physics, Xidian University – sequence: 5 givenname: Jie surname: Wang fullname: Wang, Jie organization: School of Mathematics and Statistics, Xidian University |
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| Cites_doi | 10.1016/j.camwa.2012.11.001 10.1016/S0021-8928(98)00074-4 10.1016/j.camwa.2015.11.022 10.1007/s10910-021-01216-8 10.1016/j.aml.2014.12.018 10.1016/S0024-3795(00)00289-5 10.1090/S0025-5718-1974-0371049-5 10.1016/j.aml.2014.02.015 10.12732/ijpam.v106i2.14 10.3788/CJL201845.0307018 10.1515/spma-2019-0002 10.1016/j.camwa.2015.10.018 10.1088/0266-5611/25/1/015007 10.1016/j.laa.2017.06.010 10.1007/s00211-005-0596-3 10.3390/math9243213 10.1137/0706014 10.1081/NFA-100105108 10.1016/j.jocs.2018.12.009 10.1137/0914062 |
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| Snippet | As a generalization of
k
-tridiagonal matrices, many variations of (
p
,
q
)-tridiagonal matrices have attracted much attention over the years. In this paper,... As a generalization of k-tridiagonal matrices, many variations of (p,q)-tridiagonal matrices have attracted much attention over the years. In this paper, we... |
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| SubjectTerms | Algebra Algorithms Banded structure Boundary value problems Computation Computer Science Matlab Numeric Computing Numerical Analysis Original Paper Partial differential equations Theory of Computation |
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| Title | A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices |
| URI | https://link.springer.com/article/10.1007/s11075-022-01446-0 https://www.proquest.com/docview/2918652914 |
| Volume | 93 |
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