Symbolic algorithms for the inverses of general k-tridiagonal matrices

Two symbolic algorithms for inverting k-tridiagonal matrices have been recently found by El-Mikkawy and Atlan (2014, 2015). These two algorithms are mainly based on the Doolittle LU factorization of the k-tridiagonal matrix. In the current paper, we present a new explicit analytic expression for the...

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Vydáno v:Computers & mathematics with applications (1987) Ročník 70; číslo 12; s. 3032 - 3042
Hlavní autoři: Jia, Jiteng, Li, Sumei
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.12.2015
Témata:
[formula omitted]-tridiagonal matrices
Block diagonalization
Computational cost
Inverses
Tridiagonal matrices
Tridiagonal matrices
Inverses
k-tridiagonal matrices
Computational cost
Block diagonalization
ISSN:0898-1221, 1873-7668
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Shrnutí:Two symbolic algorithms for inverting k-tridiagonal matrices have been recently found by El-Mikkawy and Atlan (2014, 2015). These two algorithms are mainly based on the Doolittle LU factorization of the k-tridiagonal matrix. In the current paper, we present a new explicit analytic expression for the inverses of general tridiagonal matrices at first. By using a block diagonalization technique, we then relate k-tridiagonal matrix inversion to tridiagonal matrix inversion. Meanwhile, an efficient algorithm is derived for computing the inverses of nonsingular k-tridiagonal matrices with the help of any algorithm for computing the inverses of tridiagonal matrices. Three examples are given in order to illustrate the performance and efficiency of the proposed algorithms.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2015.10.018