Question

4. Consider using Newton's method for the problem of minimising f(x) = |x13/2 for (a) Draw a graph of f(x) on [-1,1] to illustrate that 0 is the global minimiser b) Derive and simplify the iterative formula for Newton's method applied to this TER of f(x) problem assuming xkメ0. Use that for xメ0 the derivatives d(kl)/dx-sign x and d(sign x)/dx = 0 . (c) Show that provided 20メ0 then this Newton's iteration never converges to the minimiser 0.

can anyone help me with 4(c)

Answer 1

The function   can be shown in the graph below.

f (x)-

From the graph it can be seen that the curve intersects x-axis at ${x}=0$, i.e, solution should be 0. According to question $_{x_{o}}\neq 0$ , then by newton's method, we would need to make initial guess for $_{x_{o}}\neq 0$ . Then it would require us to make a tangent as shown in graph.

It can be seen that the function given in the question cannot converge to 0 as horizontal tangent cannot be formed through further iterations( $_{x_{1}},_{x_{2}},_{x_{3}},_{x_{4}}...$ ).

Is lo (4,8) 5 5 lo ts -S