ProcessIntermediate
What is the formula used in the Newton-Raphson iteration method to improve an approximate solution?
The formula used in the Newton-Raphson iteration method to improve an approximate solution is given by x_{n+1} = x_n - f(x_n) / f'(x_n).
Key points
- The method starts with an initial approximation x_n.
- The formula updates the approximation based on the function value and its derivative.
- Each iteration typically yields a result closer to the actual root.
Source:Advanced Engineering Mathematics· Numerical solutions of equations and interpolation· p. 41–49
Related questions
Advanced Engineering Mathematics
Stroud, K. A, Booth, Dexter J Stroud etc.
4th ed. · Industrial Press, Inc.