Accurate simple zeros of polynomials in floating point arithmetic

Stef Graillat (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

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.

Mots clés: Newton's method; zeros of polynomials; condition number; floating point arithmetic

Domaines: Analyse numérique [cs.NA]; Logiciel mathématique [cs.MS]

Stef Graillat. Accurate simple zeros of polynomials in floating point arithmetic. Computers & Mathematics with Applications, 2008, 56 (4), pp.1114-1120. ⟨10.1016/j.camwa.2008.02.027⟩. ⟨hal-00186254⟩