Accurate simple zeros of polynomials in floating point arithmetic

✍ Scribed by Stef Graillat

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 330 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2008.02.027

✦ Synopsis

In the paper, we examine the local behavior of Newton's method in floating point arithmetic for the computation of a simple zero of a polynomial assuming that an good initial approximation is available. We allow an extended precision (twice the working precision) in the computation of the residual. We prove that, for a sufficient number of iterations, the zero is as accurate as if computed in twice the working precision. We provide numerical experiments confirming this.