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nth Root extraction: Double iteration process and Newton's method

✍ Scribed by François Dubeau

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
364 KB
Volume
91
Category
Article
ISSN
0377-0427

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✦ Synopsis

A double iteration process already used to find the nth root of a positive real number is analysed and showed to be equivalent to the Newton's method. These methods are of order two and three. Higher-order methods for finding the nth root are also mentioned. (~) 1998 Elsevier Science B.V. All rights reserved.

📜 SIMILAR VOLUMES

Newton’s method and high-order algorithm
Newton’s method and high-order algorithms for the nth root computation
✍ François Dubeau 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 705 KB

Two modifications of Newton's method to accelerate the convergence of the nth root computation of a strictly positive real number are revisited. Both modifications lead to methods with prefixed order of convergence p ∈ N, p ≥ 2. We consider affine combinations of the two modified pth-order methods w