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A method for computing all the zeros of a polynomial with real coefficients

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Abstract

The problem of finding all the zeros of a polynomialP n (x)=x n+a n−1 x n−1+...+a 1 x+a 0, where the coefficientsa i are real, can be posed as a system ofn nonlinear equations. The structure of this system allows an efficient numerical solution using a damped Newton method; in particular it is possible to generate the triangular factors of the associated Jacobian matrix directly. This approach provides a natural generalisation of the well-known method of Durand and Kerner.

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Authors and Affiliations

  1. Department of Mathematics, University of Manchester, M13 9PL, Manchester, England

    T. L. Freeman

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  1. T. L. Freeman
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Freeman, T.L. A method for computing all the zeros of a polynomial with real coefficients. BIT 19, 321–333 (1979). https://doi.org/10.1007/BF01930986

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  • DOI: https://doi.org/10.1007/BF01930986

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