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Sulla determinazione della inversa delle matrici tridiagonali e tridiagonali a blocchi

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Sommario

Si espone un procedimento che consente il calcolo in una forma esplicita, abbastanza compatta, degli elementi della inversa di una qualsiasi matrice tridiagonale, con determinante diverso da zero.

I risultati sono estesi a matrici tridiagonali a blocchi con sottomatrici fra di loro commutative.

Abstract

We give here a method for the direct inversion of a tridiagonal non singular matrix. The method applies also to block-tridiagonal matrices.

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Bibliografia

  1. F. D. Burgojne,Inverse of a tridiagonal matrix, Mathematical Gazette,6 (1964), 436–437.

    Article  Google Scholar 

  2. T. S. Chow,A class of Hessemberg matrices whith known eigenvalues and inverses, SIAM Review,11 (1969) 391–395.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. A. Clement,A class of triple-diagonal matrices for test purposes, SIAM Review,1 (1959), 50–52.

    Article  MATH  MathSciNet  Google Scholar 

  4. F. W. Dorr,The direct solution of the disorete Poisson equation on a rectangle, SIAM Review,12 (1970), 248–262.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. F. Fischer, R. A. Usmani,Properties of some tridiagonal matrices and their application to boundary value problems, SIAM. J. Numer. Anal.,6 (1969) 127–142.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. T. Gregory, D. L. Karney,A collection of matrices for testing computational algorithms, Wiley-Interscience, New-York, 1969.

    Google Scholar 

  7. R. W. Hockney,A fast direct solution of Poisson's equations using Fourier analysis, J. Assoc. Comput. Mach.,12 (1965), 95–113.

    MATH  MathSciNet  Google Scholar 

  8. O. Karlquist,Numerical solution of elliptic difference equations by matrix methods, Tellus4 (1952), 374–384.

    Article  MathSciNet  Google Scholar 

  9. M. H. Lietzke, R. W. Stoughton andMarjorie P. Lietzke,A comparision of several methods for inverting large simmetric positive definite matrices,Math., Comp.,18 (1964), 449–456.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. E. Lynch, J. R. Rice andD. H. Thomas,Tensor product analysis of partial difference equation, Bull. Amer. Math. Soc.,70 (1964), 378–384.

    Article  MATH  MathSciNet  Google Scholar 

  11. R. E. Lynch, J. R. Rice andD. H. Thomas,Direct solution of difference equations by tensor product methods, Num. Math.,6 (1964), 185–199.

    Article  MATH  MathSciNet  Google Scholar 

  12. E. Merzrath,Direct solution of partial difference equations, Numer. Math.,6 (1964). 185–199.

    Article  MathSciNet  Google Scholar 

  13. M. Newman, J. Todd,The evaluation of matrix inversion programs, SIAM J. Appl. Math.,6 (1958), 466–476.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. J. Rose,An algorithm for solving a special class of tridiagonal systems of linear equations, Comm. ACM,12 (1969) 234–236.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. R. Westlake,A Handbook of numerical matrix inversion and solution of linear equations, John Wiley and Sons, Inc., New-York, 1968.

    MATH  Google Scholar 

  16. S. Zohar,Toeplitz Matrix Inversion: The algorithm of W. F. Trench, J. Assoc. Comput. Mach.,16 (1969), 502–611.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Istituto di Elaborazione della Informazione del C.N.R., Pisa

    M. Capovani

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  1. M. Capovani
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Capovani, M. Sulla determinazione della inversa delle matrici tridiagonali e tridiagonali a blocchi. Calcolo 7, 295–303 (1970). https://doi.org/10.1007/BF02575602

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  • DOI: https://doi.org/10.1007/BF02575602

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