Convergence of the Newton-Raphson’s Method

• Author(s): Lavkush Pandey
• Paper ID: 1704074
• Page: 249-259
• Published Date: 18-10-2023
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 6 Issue 8 February-2023

Abstract

Using the Newton-Raphson method, we have computed the fourth roots of natural numbers ranging from 1 to 30 and compared these results with the actual values. Our analysis reveals that the smallest error and percentage error (both being zero) were observed when calculating the fourth roots of 1 and 16. The average error was found to be 0.000000094927, while the maximum error and maximum percentage error were 0.000001154116 and 0.000097049224, respectively, for the fourth root of 2. The average percentage error is 0.000006303776. In general, the rate of numerical convergence for determining the fourth roots of numbers from 1 to 30 using the Newton-Raphson method decreases as the number increases.

Keywords

Convergence, Newton-Raphson method, Numerical accuracy, Iteration, Stopping tolerance, Approximation.

Citations

IRE Journals:
Lavkush Pandey "Convergence of the Newton-Raphson’s Method" Iconic Research And Engineering Journals Volume 6 Issue 8 2023 Page 249-259

IEEE:
Lavkush Pandey "Convergence of the Newton-Raphson’s Method" Iconic Research And Engineering Journals, 6(8)