The question of which method is more efficient, Newton's method or the secant method, was answered by Jeeves. He showed that if the effort required to evaluate f(x)' is less than 43 percent of the effort required to evaluate f(x), then Newton's method is more efficient. Otherwise, the secant method is more efficient.
The question of which method is more efficient, Newton's method or the secant method, was answered by Jeeves. He showed that if the effort required to evaluate f(x)' is less than 43 percent of the effort required to evaluate f(x), then Newton's method is more efficient. Otherwise, the secant method is more efficient.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLEASE SHOW A COMPLETE AND UNDERSTANDABLE SOLUTION. THANK YOU!!
![Example for y =x - cos(x) on [0.0,4.0] for eps = 1.0e-6
initial point is 1.0
iterations
root
0.73909
5
for bisectional method it takes 22 iterations, but for
Newton only 4 iterations.
The question of which method is more efficient, Newton's
method or the secant method, was answered by Jeeves.
He showed that if the effort required to evaluate f(x)' is
less than 43 percent of the effort required to evaluate f(x),
then Newton's method is more efficient. Otherwise, the
secant method is more efficient.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10dd63ff-731a-4478-a018-881e433c8250%2Fa23e52da-ae35-4bb8-8b02-d0e1beaf1865%2Fguag3ya_processed.png&w=3840&q=75)
Transcribed Image Text:Example for y =x - cos(x) on [0.0,4.0] for eps = 1.0e-6
initial point is 1.0
iterations
root
0.73909
5
for bisectional method it takes 22 iterations, but for
Newton only 4 iterations.
The question of which method is more efficient, Newton's
method or the secant method, was answered by Jeeves.
He showed that if the effort required to evaluate f(x)' is
less than 43 percent of the effort required to evaluate f(x),
then Newton's method is more efficient. Otherwise, the
secant method is more efficient.
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