Q 2: Halley's iterative method for solving a nonlinear equation f(x) = 0 can be written as 2f(xn)f'(xn) Xn+1 = X - n 20

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q 2: Halley's iterative method for solving a nonlinear equation f(x) = 0 can be written as
2f(xn)f'(xn)
F(x-f(x)f"(x,)'
Xn+1 = X -
n20
Show that Halley's iterative formula for computing the square root of a positive number K can be written as
3Kx, - x
Xn+1 =
x + K
n20
Also, show that the rate of convergence of the last scheme is faster than quadratic.
Transcribed Image Text:Q 2: Halley's iterative method for solving a nonlinear equation f(x) = 0 can be written as 2f(xn)f'(xn) F(x-f(x)f"(x,)' Xn+1 = X - n20 Show that Halley's iterative formula for computing the square root of a positive number K can be written as 3Kx, - x Xn+1 = x + K n20 Also, show that the rate of convergence of the last scheme is faster than quadratic.
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