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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) Xn+1 = X - n 20

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 17E
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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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