search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
5 votes
953 views

The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$  is the derivative of $f$. The method converges

  1. always
  2. only if $f$ is a polynomial
  3. only if $f(x_o) <0$
  4. none of the above
in Numerical Methods
edited by
953 views

2 Answers

3 votes
 
Best answer

Answer: D

The method will usually converge, provided this initial guess is close enough to the unknown zero, and that f$'$(x0) != 0.

0 votes
Ans D
Answer:

Related questions

4 votes
2 answers
1
768 views
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$
asked Oct 9, 2014 in Numerical Methods Kathleen 768 views
0 votes
0 answers
2
668 views
A piecewise linear function $f(x)$ is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of \(f(x)=0\) using \(x_0, x_1,\) and \(x_2\) respectively as initial guesses, the roots obtained would be ... and 0.6 respectively 0.6, 0.6, and 1.3 respectively 1.3, 1.3, and 0.6 respectively 1.3, 0.6, and 1.3 respectively
asked Sep 17, 2014 in Numerical Methods Kathleen 668 views
1 vote
1 answer
3
1.5k views
The Newton-Raphson iteration $x_{n+1} = \frac{1}{2}\left(x_n+\frac{R}{x_n}\right)$ can be used to compute the square of R reciprocal of R square root of R logarithm of R
asked Sep 12, 2014 in Numerical Methods Kathleen 1.5k views
1 vote
0 answers
4
409 views
Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to 1.5 $\sqrt{2}$ 1.6 1.4
asked Sep 22, 2014 in IS&Software Engineering Kathleen 409 views
...