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A new method for solving ill-conditioned linear systems

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in MATHEMATICA 7.
Rocznik
Strony
337--344
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
  • Islamic Azad University Department of Mathematics Zahedan Branch, Zahedan, Iran
Bibliografia
  • [1] E. Chow, Y. Saad, Approximate inverse preconditioned via sparse-sparse iterations. SIAM J. Sci. Comput. 19 (1998), 995-1023.
  • [2] G. Codevico, V.Y. Pan, M.V. Barel, Newton-Like iteration based on a cubic polynomial for structured matrices, Numer. Algorithms 36 (2004), 365-380.
  • [3] E.V. Krishnamurthy, S.K. Sen, Numerical Algorithms - Computations in Science and Engineering, Affiliated East-West Press, New Delhi, 1986.
  • [4] H.-B. Li, T.-Z. Huang, Y. Zhang, V.-P. Liu, T.-V. Gu, Chebyshev-type methods and preconditioning techniques, Appl. Math. Comput. 218 (2011), 260-270.
  • [5] W. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Appl. Math. Comput. 215 (2010), 3433-3442.
  • [6] C.-S. Liu, W. Yeih, S.N. Atluri, On solving the ill-conditioned system Ax = b: General-purpose conditioners obtained from the boundary-collocation solution of the Laplace equation, using Trefftz expansions with multiple length scales, CMES Comput. Model. Eng. Sci. 44 (2009), 281-311.
  • [7] K. Moriya, T. Noderab, A new scheme of computing the approximate inverse precondi-tioner for the reduced linear systems, J. Comput. Appl. Math. 199 (2007), 345-352.
  • [8] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, 2003.
  • [9] G. Schulz, Iterative Berechnung der Reziproken Matrix, Z. Angew. Math. Mech. 13 (1933), 57-59.
  • [10] S.K. Sen, S.S. Prabhu, Optimal iterative schemes for computing Moore-Penrose matrix inverse, Int. J. Systems Sci. 8 (1976), 748-753.
  • [11] S. Wolfram, The Mathematica Book, 5th ed., Wolfram Media, 2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cb04230f-566c-445e-90fc-f4aaf3fa08cb
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