A) Calculate the square root of the number 9 by the fixed point iteration method and Newton-Raphson, providing a suitable iteration function, to the nearest 2 decimal places. (Tip: To calculate the square root of 9, you must solve the equation x² – 9 = 0)
A) Calculate the square root of the number 9 by the fixed point iteration method and Newton-Raphson, providing a suitable iteration function, to the nearest 2 decimal places. (Tip: To calculate the square root of 9, you must solve the equation x² – 9 = 0)
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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Question
S3
Transcribed Image Text:A) Calculate the square root of the number 9 by the fixed point iteration method
and Newton-Raphson, providing a suitable iteration function, to the nearest 2
decimal places.
(Tip: To calculate the square root of 9, you must solve the equation x? – 9 = 0)
B) Since we know the square root of 9 exactly, we can calculate the actual error at
each step. Inspired by Figure 8-2, compare the convergence velocities of both
methods using the error curve for the number of repetitions.
10
10 1
10-2
10-3
10-4
10-5
10-8
20
Iterations
Figure 8-2: Comparison of convergence velocities in two-part methods, misalignment, chord and
Newton-Raphson (Source: Chapra book)
Bisection
False position
Secant
Newton-Raphson
True percent relative error
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