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Volume 14 Issue 5
September  1999
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ZHANG Shugong, LIU Ying, FENG Guochen. The Multiplicity of Zeros of Algebraic System in Eigenvalue Method[J]. Journal of Computer Science and Technology, 1999, 14(5): 510-517.
Citation: ZHANG Shugong, LIU Ying, FENG Guochen. The Multiplicity of Zeros of Algebraic System in Eigenvalue Method[J]. Journal of Computer Science and Technology, 1999, 14(5): 510-517.
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The Multiplicity of Zeros of Algebraic System in Eigenvalue Method

  • Institute of Mathematics; Jilin University; Changchun 130023 P.R. China ;

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  • Published Date: September 09, 1999
    Abstract
  • This article deals with the structure relations between solutions toalgebraic system and matrices in eigenvalue method for solving the algebraic system-The authors first discuss the condition on the ideal generated by the given systemunder which the eigenspace of matrix has dimension 1 since in this case the zerocan be easily found. Then they study the relations between the multiplicity of zerosof the given system and orders of Jordan blocks of matrices formed in eigenvaluemethod.
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    • References (3)
  • [1]
    Auzinger W, Stetter H J. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations. In Conference in Numerical Analysis, ISNM 88, 11-30, Birkhauser Verlag, 1988.
    [2]
    Feng Guochen, Zhang Shugong. Reducing the multivariate polynomial system to eigenvalue problem. Northeastern Math.J., 1992, 8(3): 253-256.
    [3]
    Feng Guochen, Wu Wenda and Zhang Shugong. The eigenvalue problem equivalent to multivariate polynomial system. Nu}nericad Mathematics, A J. of Chinese Universities, 1993, 2(2): 234-241. ……….
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