It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further, it is given that the root r is a root of multiplicity 2, i.e., f(x) = (x – r)² g(x), where g(r) + 0. It is also given that the function f, its derivatives till the second order are continuous in the neighbourhood of the root r. If en is the error of the nth iterate, i.e., en = xn – r, then obtain en+1 lim en n00
It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further, it is given that the root r is a root of multiplicity 2, i.e., f(x) = (x – r)² g(x), where g(r) + 0. It is also given that the function f, its derivatives till the second order are continuous in the neighbourhood of the root r. If en is the error of the nth iterate, i.e., en = xn – r, then obtain en+1 lim en n00
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:It is given that a sequence of Newton iterates converge to a root r of the function f(x). Further,
it is given that the root r is a root of multiplicity 2, i.e., f(x) = (x – r)² g(x), where g(r) # 0. It is also
given that the function f, its derivatives till the second order are continuous in the neighbourhood of the
root r. If en is the error of the nth iterate, i.e.., en = xn – r, then obtain
en+1
lim
n-00
en
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