Journal of the Korean Society for Industrial and Applied Mathematics

  • 제24권3호
  • /
  • Pages.305-320
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  • 2020
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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A METHOD FOR SOLVING OF LINEAR SYSTEM WITH NORMAL COEFFICIENT MATRICES

  • KAMALVAND, M.GHASEMI (DEPARTMENT OF MATHEMATICAL SCIENCES, LORESTAN UNIVERSITY) ;
  • FARAZMANDNIA, B. (DEPARTMENT OF MATHEMATICAL SCIENCES, LORESTAN UNIVERSITY) ;
  • ALIYARI, M. (DEPARTMENT OF MATHEMATICAL SCIENCES, AYATOLLAH BORUJERDI UNIVERSITY)
  • 투고 : 2020.05.17
  • 심사 : 2020.09.14
  • 발행 : 2020.09.25
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초록

This study aims to generalize MINRES-N2 method [1]. It means that we tend to obtain an algorithm to transfer each normal matrix - that its eigenvalues belong to an algebraic curve of low degree k- to its condensed form through using a unitary similarity transformation. Then, we aim to obtain a method to solve a system of linear equations that its coefficient matrix is equal to such a matrix by utilizing it. Finally this method is compared to the well-known GMRES method through using numerical examples. The results obtained through examples show that the given method is more efficient than GMRES.

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참고문헌

  1. L. Elsner and Kh.D. Ikramov, On a condensed form for normal matrices under finite sequences of elementary unitary similarities. - Linear Algebra Appl., 254 (1997) 79-98. https://doi.org/10.1016/S0024-3795(96)00526-5
  2. M. Dana, Kh. D. Ikramov, On low rank perturbations of the Hermitian and unitary matrices. - Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004), 1331-1345.
  3. M. Ghasemi Kamalvand, Kh. D. Ikramov, A Method of Congruent Type for Linear Systems with Conjugate-Normal Coefficient Matrices. - Computational Mathematics and Mathematical Physics, 2009, Vol. 49, No. 2, pp. 203-216. https://doi.org/10.1134/S0965542509020018
  4. M. Ghasemi Kamalvand, Kh. D. Ikramov, Low-Rank Perturbations of Symmetric Matrices and Their Condensed Forms under Unitary Congruences. - Computational Mathematics and Mathematical Physics, 2009, Vol. 49, No. 4, pp. 573-578. https://doi.org/10.1134/S0965542509040010
  5. M. Ghasemi Kamalvand, Kh. D. Ikramov, Low-Rank Perturbations of Normal and Conjugate-Normal Matrices and Their Condensed Forms under Unitary Similarities and Congruences. - Moscow University Computational Mathematics and Cybernetics, 2009, Vol. 33, No. 3, pp. 109-116. https://doi.org/10.3103/S0278641909030017
  6. K.Niazi Asil, M. Ghasemi Kamalvand, On Reduction of K-Almost Normal and K-Almost Conjucate Normal Matrices to a Block Tridiagonal Form. - J. Korean Soc. Ind. Appl. Math. Vol.23, No.3, 267-282, 2019. https://doi.org/10.12941/jksiam.2019.23.267
  7. M. Dana, A. G. Zykov, Kh.D. Ikramov, A minimal residual method for a special class of the linear systems with normal coefficient matrices. - Comput. Math. Math. Phys., 45 (2005) 1854-1863.
  8. R.A. Horn and C.R. Johnson, Matrix Analysis. Cambridge University Press, Cambridge, 1985.