(Q5) Clearly P = r is a root of f(x) = (7 – x) sin(x – 7). (a) Find the multiplicity of this root. (b) Find the order of convergence and the asymptotic error constant if we used Newton-Raphson...

(Q5) Clearly P = r is a root of f(x) = (7 – x) sin(x – 7).<br>(a) Find the multiplicity of this root.<br>(b) Find the order of convergence and the asymptotic error constant if we used Newton-Raphson iteration to<br>estimate this root.<br>(c) Use the accelerated Newton's method to estimate this root using Po = 3. Find two iterations.<br>(d) What is the order of convergence and the asymptotic error constant for bisection method to estimate this root?<br>(e) What is the order of convergence of secant method to estimate this root?<br>(f) What is the order of convergence of false-position method to estimate this root?<br>

Extracted text: (Q5) Clearly P = r is a root of f(x) = (7 – x) sin(x – 7). (a) Find the multiplicity of this root. (b) Find the order of convergence and the asymptotic error constant if we used Newton-Raphson iteration to estimate this root. (c) Use the accelerated Newton's method to estimate this root using Po = 3. Find two iterations. (d) What is the order of convergence and the asymptotic error constant for bisection method to estimate this root? (e) What is the order of convergence of secant method to estimate this root? (f) What is the order of convergence of false-position method to estimate this root?

Jun 05, 2022

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(Q5) Clearly P = r is a root of f(x) = (7 – x) sin(x – 7). (a) Find the multiplicity of this root. (b) Find the order of convergence and the asymptotic error constant if we used Newton-Raphson...

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