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The multiplicity of zeros of algebraic system in eigenvalue method

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Abstract

This article deals with the structure relations between solutions to algebraic system and matrices in eigenvalue method for solving the algebraic system. The authors first discuss the condition on the ideal generated by the given system under which the eigenspace of matrix has dimension 1 since in this case the zero can be easily found. Then they study the relations between the multiplicity of zeros of the given system and orders of Jordan blocks of matrices formed in eigenvalue method.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, 130023, Changchun, P.R. China

    Zhang Shugong, Liu Ying & Feng Guochen

Authors
  1. Zhang Shugong
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  2. Liu Ying
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  3. Feng Guochen
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Corresponding author

Correspondence to Zhang Shugong.

Additional information

ZHANG Shugong was born in 1958. He joined Northeast Institute of Technology (now renamed as Northeast University) in 1978. In 1993, he got his Ph.D. degree from Jilin University. Now he is an Associate Professor of Mathematics Department of Jilin University. His research interests include numerical analysis and computer mathematics.

LIU Ying was born in 1963. He began his study in Mathematics Department of Jilin University in 1984 and got his Ph.D. degree in 1995. He works now as an Associate Professor in Math. Dept. of Tsinghua University, and does researches in field of numerical analysis.

FENG Guochen was born in 1935. He joined Jilin University in 1956. Since 1957 he has been working in Jilin University. He is now a Professor of Math. Dept. His research interests include numerical analysis, computer mathematics, etc.

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Zhang, S., Liu, Y. & Feng, G. The multiplicity of zeros of algebraic system in eigenvalue method. J. Comput. Sci. & Technol. 14, 510–517 (1999). https://doi.org/10.1007/BF02948792

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  • DOI: https://doi.org/10.1007/BF02948792

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