Accurate simple zeros of polynomials in floating point arithmetic

Stef Graillat 1
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : In the paper, we examine the behavior of the Newton's method in floating point arithmetic for the computation of a simple zero of a polynomial. We allow an extended precision (twice the working precision) in the computation of the residual. We prove that, for a sufficient number of iteration, the zero is as accurate as if computed in twice the working precision. We provides numerical experiments confirming this.
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Stef Graillat. Accurate simple zeros of polynomials in floating point arithmetic. Computers and Mathematics with Applications, Elsevier, 2008, 56 (4), pp.1114-1120. ⟨10.1016/j.camwa.2008.02.027⟩. ⟨hal-00186254⟩

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