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Inverting a k-heptadiagonal matrix based on Doolitle LU factorization

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Abstract

The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix. This work is based on Doolitle LU factorization of the matrix. We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix. The computational cost of the algorithm is calculated. Some illustrative examples are given to demonstrate the effectiveness of the proposed method.

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References

  1. M El-Mikkawy. A fast algorithm for evaluating nth order tri-diagonal determinants. Journal of Computational and Applied Mathematics, 2004, 166(2): 581–584.

    Article  MathSciNet  Google Scholar 

  2. M El-Mikkawy. A Generalized Symbolic Thomas Algorithm, Applied Mathematics, 2012, 3: 342–345.

    Article  MathSciNet  Google Scholar 

  3. M El-Mikkawy, F Atlan. A novel algorithm for inverting a general k-tridiagonal matrix, Applied Mathematics Letters, 2014, 32: 41–47.

    Article  MathSciNet  Google Scholar 

  4. M El-Mikkawy, A Karawia. Inversion of general tridiagonal matrices. Applied Mathematics Letters, 2006, 19(8): 712–720.

    Article  MathSciNet  Google Scholar 

  5. J Jia, S Li. Symbolic algorithms for the inverses of general k-tridiagonal matrices. Computers and Mathematics with Applications, 2015, 70(12): 3032–3042.

    Article  MathSciNet  Google Scholar 

  6. J Jia, S Li. New algorithms for numerically solving a class of bordered tridiagonal systems of linear equations. Computers and Mathematics with Applications, 2019, 78(1): 144–151.

    Article  MathSciNet  Google Scholar 

  7. J Jia, T Sogabe, M El-Mikkawy. Inversion of k-tridiagonal matrices with Toeplitz structure. Computers and Mathematics with Applications, 2013, 65(1): 116–125.

    Article  MathSciNet  Google Scholar 

  8. X Zhao, T Huang. On the inverse of a general pentadiagonal matrix. Applied Mathematics and Computation, 2008, 20(2): 639–646.

    Article  MathSciNet  Google Scholar 

  9. Y Lin, X Lin. A novel algorithm for inverting a k-pentadiagonal matrix, The 2016 3rd International Conference on Systems and Informatics (ICSAI 2016), 2016, 578–582.

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Authors and Affiliations

  1. Department of mathematics, Payamenoor university, Tehran, Iran

    Maryam Shams Solary & Mehran Rasouli

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  1. Maryam Shams Solary
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  2. Mehran Rasouli
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Correspondence to Maryam Shams Solary or Mehran Rasouli.

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Solary, M.S., Rasouli, M. Inverting a k-heptadiagonal matrix based on Doolitle LU factorization. Appl. Math. J. Chin. Univ. 37, 340–349 (2022). https://doi.org/10.1007/s11766-022-3763-8

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  • DOI: https://doi.org/10.1007/s11766-022-3763-8

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