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Topics in Numerical Analysis pp 227–238Cite as

An Explicit Inversion Formula for Tridiagonal Matrices

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Part of the book series: Computing Supplementa ((COMPUTING,volume 15))

Abstract

Discretizing two-point boundary value problems on an interval by finite difference method, we obtain a certain type of tridiagonal coefficient matrices. In this paper we give an explicit inversion formula for such tridiagonal matrices using Yamamoto-Ikebe’s inversion formula.

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References

  1. Fang, Q., Tsuchiya, T., Yamamoto, T.: Finite difference, finite element and finite volume methods applied to two-point boundary value problems. J. Comp. Appl. Math, (to appear).

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  2. Meurant, G.: A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM J. Matrix Anal. Appl. 13, 707–728 (1992).

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  3. Tsuchiya, T., Yoshida, K.: An application of Yamamoto’s explicit inversion formula for tridiagonal matrices to finite element error analysis (in preparation).

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  4. Yamamoto, T.: A new insight of the Shortley-Weller approximation for Dirichlet problems. In: Dagstuhl Proceedings of the Seminar’ Symbolic Algebraic Methods and Verification Methods’ (Alefeld, G., et al., eds.), pp. 245–253. Berlin Heidelberg New York Tokyo: Springer, 2001.

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  5. Yamamoto, T.: Inversion formulas for tridiagonal matrices with applications to boundary value problems. In: Numer. Funct. Anal. Optim. 22 (in press).

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  6. Yamamoto, T., Ikebe, Y.: Inversion of band matrices. Linear Algebra Appl. 24, 105–111 (1979).

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  7. Yoshida, K.: Error analysis of the Shortley-Weiler finite difference method applied to two-point boundary value problems (in preparation).

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  8. Yoshida, K., Tsuchiya, T.: Recovered derivatives for the Shortley-Weiler finite difference approximation (submitted).

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama, 790-8577, Japan

    T. Tsuchiya & Q. Fang

Authors
  1. T. Tsuchiya
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  2. Q. Fang
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

    Goetz Alefeld

  2. Department of Mathematical Sciences, Shimane University, Matsue, Japan

    Xiaojun Chen

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© 2001 Springer-Verlag Wien

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Tsuchiya, T., Fang, Q. (2001). An Explicit Inversion Formula for Tridiagonal Matrices. In: Alefeld, G., Chen, X. (eds) Topics in Numerical Analysis. Computing Supplementa, vol 15. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6217-0_17

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  • DOI: https://doi.org/10.1007/978-3-7091-6217-0_17

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83673-6

  • Online ISBN: 978-3-7091-6217-0

  • eBook Packages: Springer Book Archive

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