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Solving triangular algebraic systems by means of simultaneous iterations

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Abstract

Our aim in this paper is to extend a variant of the Weierstrass method for the simultaneous computation of the solutions of a triangular algebraic system of equations. The appropriate tools are the symmetric functions of the roots of a polynomial. Using these symmetric functions we give another equivalent formulation for the search of all the roots of a triangular algebraic system. Using the latter formulation our method consists in solving a more simple system (where partial degrees of all the equations do not exceed 1) by Newton’s method. The quadratic convergence of our method is an immediate consequence of Newton’s method and need not be proved explicitly.

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Authors and Affiliations

  1. L3MA-SP2MI, Université de Poitiers, Boulevard 3, Téléport 2, B.P. 179, F-86960, Futuroscope Cedex, France

    Alain Piétrus

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  1. Alain Piétrus
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Piétrus, A. Solving triangular algebraic systems by means of simultaneous iterations. Numerical Algorithms 20, 353–368 (1999). https://doi.org/10.1023/A:1019124405774

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  • DOI: https://doi.org/10.1023/A:1019124405774

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