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ajprincess
Group Title
Please help:)
By applying NewtonRaphson method to \(f(x)=1\large\frac{1}{ax}\) obtain the recurrence formula \(x_{i+1}=x_i(2ax_i)\) for the iterative determination of the reciprocal of a. Show that if \(E_i\) denotes the error in the \(x_i\), there follows \(E_{i+1}=a{E_i}^2\).
 2 years ago
 2 years ago
ajprincess Group Title
Please help:) By applying NewtonRaphson method to \(f(x)=1\large\frac{1}{ax}\) obtain the recurrence formula \(x_{i+1}=x_i(2ax_i)\) for the iterative determination of the reciprocal of a. Show that if \(E_i\) denotes the error in the \(x_i\), there follows \(E_{i+1}=a{E_i}^2\).
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[x_{i+1}=x_i\frac{f(x_i)}{f'(x_i)}\] \[x_{i+1}=x_i\frac{1\frac{1}{ax}}{\frac{1}{ax^2}}\]and some algebra should work
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i guess it should be \[x_{i+1}=x_i\frac{1\frac{1}{ax_i}}{\frac{1}{ax_i^2}}\]
 2 years ago

ajprincess Group TitleBest ResponseYou've already chosen the best response.0
Ya I have proved that part. I need help with the error part
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
nope i am wrong again it should be \[x_{i+1}=x_i\frac{1\frac{1}{ax_i}}{\frac{1}{ax_i^2}}\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i think it has something to do with taylor series, but i should really shut up
 2 years ago

ajprincess Group TitleBest ResponseYou've already chosen the best response.0
ohh that's k. Thankk u sooo much for helping me:)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
on second page for "division"
 2 years ago

ajprincess Group TitleBest ResponseYou've already chosen the best response.0
Thankkkk u sooooo much. It is really verryy useful:)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yw, and good luck
 2 years ago

ajprincess Group TitleBest ResponseYou've already chosen the best response.0
thank u:)
 2 years ago
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