ajprincess
  • ajprincess
Please help:) By applying Newton-Raphson method to \(f(x)=1-\large\frac{1}{ax}\) obtain the recurrence formula \(x_{i+1}=x_i(2-ax_i)\) for the iterative determination of the reciprocal of a. Show that if \(E_i\) denotes the error in the \(x_i\), there follows \(E_{i+1}=-a{E_i}^2\).
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
\[x_{i+1}=x_i-\frac{f(x_i)}{f'(x_i)}\] \[x_{i+1}=x_i-\frac{1-\frac{1}{ax}}{-\frac{1}{ax^2}}\]and some algebra should work
anonymous
  • anonymous
i guess it should be \[x_{i+1}=x_i-\frac{1-\frac{1}{ax_i}}{-\frac{1}{ax_i^2}}\]
ajprincess
  • ajprincess
Ya I have proved that part. I need help with the error part

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
nope i am wrong again it should be \[x_{i+1}=x_i-\frac{1-\frac{1}{ax_i}}{\frac{1}{ax_i^2}}\]
anonymous
  • anonymous
damn i wish i could help, but i don't know an expression for the error. newton ralphson is always error squaring, i know that much but i am not sure how to prove it
anonymous
  • anonymous
i think it has something to do with taylor series, but i should really shut up
ajprincess
  • ajprincess
ohh that's k. Thankk u sooo much for helping me:)
anonymous
  • anonymous
on the other hand i am pretty good at googling. try looking at "error analysis" in the attached pdf, seems like exactly what you are looking for
1 Attachment
anonymous
  • anonymous
on second page for "division"
ajprincess
  • ajprincess
Thankkkk u sooooo much. It is really verryy useful:)
anonymous
  • anonymous
yw, and good luck
ajprincess
  • ajprincess
thank u:)

Looking for something else?

Not the answer you are looking for? Search for more explanations.