Physics of Particles and Nuclei Letters

, Volume 5, Issue 3, pp 181–184 | Cite as

Properties of generalized matrix sequence

  • E. B. Dushanov


In case of block-tridiagonal matrix, the problem of calculation of a generalized double-point matrix sequence is examined. The general form of inverse matrix of the bordered matrix is obtained when the initial matrix is singular. The criterion of existence of the generalized matrix sequence is found, and the algorithm of calculation of the sequence and the structure elements of the block-tridiagonal matrices are given.

PACS numbers

02.10.Yn 02.60.-x 


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  1. 1.
    V. N. Malozemov, M. F. Monako, and A. V. Petrov, “Frobenius, Sherman-Morrison Formulas and Simular Problems,” J. Vich. Mat. Mat. Fiz. 42, 1459–1465 (2002).MATHMathSciNetGoogle Scholar
  2. 2.
    G. A. Emeljyanenko, T. T. Rakhmonov, and E. B. Dushanov, “Critical—Component Method for Solving Systems of Linear Equations with a Tridiagonal Matrix of the General Form,” JINR Preprint E11-96-105 (Dubna, 1996).Google Scholar
  3. 3.
    D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, 2nd ed. (Fizmatgiz, Moscow, 1963; Freeman, San Francisco, 1963).Google Scholar
  4. 4.
    V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Computations (Nauka, Moscow, 1984) [in Russian].MATHGoogle Scholar
  5. 5.
    J. Rice, Matrix Computations and Mathematical Software (McCraw-Hill, 1981).Google Scholar
  6. 6.
    G. A. Emeljyanenko and T. T. Rakhmonov, “Generators of Matrix-Factorized Representations of Block-Tridiagonal Matrices and Heir Inverces,” JINR Preprint P11-93-265 (Dubna, 1993).Google Scholar
  7. 7.
    F. R. Gantmakher, Theory of Matrices, 2nd ed. (Nauka, Moscow, 1966) [in Russian].Google Scholar
  8. 8.
    G. H. Golub and Ch. F. van Loan, Matrix Computations (John Hopkins Univ. Press, 1989).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • E. B. Dushanov
    • 1
  1. 1.Institute of Nuclear PhysicsTashkentUzbekistan

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