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An adaptive multiprecision algorithm for univariate polynomial zeros

D. Bini
G. Fiorentino
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 53-60

We present an adaptive multiprecision poly-algorithm for the approximation of all the roots of polynomials with complex coefficients whose real and imaginary parts can be integer, rational or floating point numbers. The algorithm for the simultaneous approximation of all the roots relies on some specific convergence properties of Aberth's and Durand-Kerner's methods and uses a criterion based on Touche's theorem to select good starting approximations. The algorithm has been coded in Mathematica and numerical experiments show that it is more robust and in most cases faster than the built-in function VSolve.

*Mathematics > Algebra > Polynomials