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An approach to solving nonlinear algebraic systems. 2

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Abstract

New methods of solving nonlinear algebraic systems in two variables are suggested, which make it possible to find all zero-dimensional roots without knowing initial approximations. The first method reduces the solution of nonlinear algebraic systems to eigenvalue problems for a polynomial matrix pencil. The second method is based on the rank factorization of a two-parameter polynomial matrix, allowing, us to compute the GCD of a set of polynomials and all zero-dimensional roots of the GCD. Bibliography: 10 titles.

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Literature Cited

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Authors
  1. V. N. Kublanovskaya
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  2. V. N. Simonova
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Translated by V. N. Kublanovskaya

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 71–96

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Kublanovskaya, V.N., Simonova, V.N. An approach to solving nonlinear algebraic systems. 2. J Math Sci 79, 1077–1092 (1996). https://doi.org/10.1007/BF02366128

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  • DOI: https://doi.org/10.1007/BF02366128

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