대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제40권3호
  • /
  • Pages.425-435
  • /
  • 2003
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EFFICIENT ALGORITHMS FOR COMPUTING THE MINIMAL POLYNOMIALS AND THE INVERSES OF LEVEL-k Π-CIRCULANT MATRICES

  • Jiang, Zhaolin (Department of Applied Mathematics, Xidian University) ;
  • Liu, Sanyang (Department of Applied Mathematics, Xidian University)
  • 발행 : 2003.08.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a new kind of matrices, i.e., $level-{\kappa}$ II-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Grobner basis of the ideal in the polynomial ring. Two algorithms for finding the inverses of such matrices are also presented based on the Buchberger's algorithm.

키워드

참고문헌

  1. Amer. Math. Soc. An introduction to Grobner bases W.W.Adams;P.Loustaunau
  2. Amer. Math. Monthly. v.62 Methods of matrix inversion D.Greenspan https://doi.org/10.2307/2307034
  3. J. London Math. Soc. v.8 Injective envelopes and inverse polynomials D.G.Northcott
  4. J. Algebra v.100 New constructive methods in classical ideal theory H.M.Moller;F.Mora https://doi.org/10.1016/0021-8693(86)90071-2
  5. Circulant Matrices J.Zhaolin;Z.Zhangxin
  6. Kyung-pook Math. J. v.25 The structure of multiblock circulants J.Baker;F.Hiergeist;G.Trapp
  7. J. Combin. Theory, Series A v.40 Construction of D-optimal designs for N=2 mod 4 using block-circulant matrices TH.Chadjipantelis;STR.Kounias;CHR.Moyssiadis https://doi.org/10.1016/0097-3165(85)90051-2
  8. Algorithmic Algebra B.Mishra

피인용 문헌

  1. Inversion of two new circulant matrices over Zm vol.81, 2017, https://doi.org/10.1088/1755-1315/81/1/012200