Explore BrainMass

# Real Analysis - Newton's Method and showing convergence.

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Newton's Method: Consider the equation f(x)=0 where f is a real-valued function of a real variable. Let x_0 be any initial approximation of the solution and let
x_(n+1)=x_n - (f(x_n)/f'(x_n)).
Show that if there is a positive number "a" such that for all x in [x_0-a, x_0+a]
|(f(x)f''(x))/((f'(x))^2)|<=lambda<1 and
|(f(x_0))/(f'(x_0))|<=(1-lamda)a
then the sequence (x_n) converges to a solution of f(x)=0.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:12 pm ad1c9bdddf
https://brainmass.com/math/real-analysis/real-analysis-newtons-method-showing-convergence-87794

#### Solution Summary

Newton's Method and convergence are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

\$2.49