3. Newton's method Let f:R → R be given by f(x):= { x - a3, where a € R is a constant. The minimizer is obviously * = a. Suppose that we apply Newton's method to the following problem: minimize f(x):= |x — a als from an initial point 2" ER {a}. (a) (3 points) Write down f'(x) and F"(x). You need to consider two cases: < > a and x <a. (b) (2 points) Write down the update equation...
does anyone knows how to do 4(C)?
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...
can anyone help me with 4(c)
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...
detailed answer and thumbs up guaranteed
Newton's method Let f: R + R be given by f(x) := }\x – al, where a € R is a constant. The minimizer is obviously 2* = a. Suppose that we apply Newton's method to the following problem: minimize f(x):= با این | 2 – al: from an initial point x° ER \ {a}. (a) (3 points) Write down f'(x) and f'(). You need to consider two cases: < > a and x...
2. The Good, the Bad, and the Ugly Initial Approximations The x-intercept of x) 6r-28r+16r 2 is shown in the graph below a) Find and simplify the formula from Newton's Method for calculating b) Use the formula you found above and the initial approximation -0.4 to approximate the value of the x-intercept, correct to five decimal places c) Repeat using the initial approximation x-05. What happens? d) Repeat using the initial approximation x-0.6. What happens? Other Applications of Newton's Method...
[10 pts] Use Newton's method to approximate root x, of f(x)-x-5 assuming 0
[10 pts] Use Newton's method to approximate root x, of f(x)-x-5 assuming 0
Uan Newton's method to calculator x for f(x) = 2x' + 8 pven that x = 2 x2=1.00 *2=125 X: 050
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
12. Let f: x> (x-1)2-1. (a) Apply fixed-point iteration to f with ro-1. What is the next iterate? (b) Apply Newton's method to f with ro- 1. What is the next iterate? (c) Apply the secant method to f with 20 1 andェ,-2. What is the next iterate? CD
12. Let f: x> (x-1)2-1. (a) Apply fixed-point iteration to f with ro-1. What is the next iterate? (b) Apply Newton's method to f with ro- 1. What is the next...
2. (a) Explain Newton's Method, which lets you improve approximations to roots of a function f(x) by following the tangent line down to the x-axis. (b) What if, instead of following a best fit straight line, you were to follow a best fit parabola? What's the equation of this parabola, and of its intersection with the x-axis? Compared with Newton's Method, how quickly do the approximate roots computed using this method typically converge to the exact root? (c) The method...