Question

If we want to minimize a function f(x) = e^(x^2) over R, then it is equivalent...

If we want to minimize a function f(x) = e^(x^2)
over R, then it is equivalent to finding the root of f '(x). Starting with x0 = 1, can you perform 4 iterations of Newton's method to estimate the minimizer
of f(x)? (Correct to four decimal places at each iteration).

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For the following function, determine the highest real root of f(x) = 2x3 – 11.7x2 +...
For the following function, determine the highest real root of f(x) = 2x3 – 11.7x2 + 17.7x - 5 by using (a) graphical methods, (b) fixed point iteration (three iterations, x0 = 3) (Hint: Be certain that you develop a solution that converges on the root), and (c) Newton-Raphson method (three iterations, x0 = 3). Perform an error check on each of your final root approximations (e.g. for the last of the three iterations).
Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3 a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0....
Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3 a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0. b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094. Show that this ratio's value approaches |?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges quadratically). In error computation, keep as many digits as you can.
Consider the function g (x) = 12x + 4 - cos x. Given g (x) =...
Consider the function g (x) = 12x + 4 - cos x. Given g (x) = 0 has a unique solution x = b in the interval (−1/2, 0), and you can use this without justification. (a) Show that Newton's method of starting point x0 = 0 gives a number sequence with b <··· <xn+1 <xn <··· <x1 <x0 = 0 (The word "curvature" should be included in the argument!) (b) Calculate x1 and x2. Use theorem 2 in section...
Consider the function g (x) = 12x + 4 - cos x. Given g (x) =...
Consider the function g (x) = 12x + 4 - cos x. Given g (x) = 0 has a unique solution x = b in the interval (−1/2, 0), and you can use this without justification. (a) Show that Newton's method of starting point x0 = 0 gives a number sequence with b <··· <xn+1 <xn <··· <x1 <x0 = 0 (The word "curvature" should be included in the argument!) (b) Calculate x1 and x2. Use theorem 2 in section...
Consider the function g (x) = 12x + 4 - cos x. Given g (x) =...
Consider the function g (x) = 12x + 4 - cos x. Given g (x) = 0 has a unique solution x = b in the interval (−1/2, 0), and you can use this without justification. (a) Show that Newton's method of starting point x0 = 0 gives a number sequence with b <··· <xn+1 <xn <··· <x1 <x0 = 0 (The word "curvature" should be included in the argument!) (b) Calculate x1 and x2. Use theorem 2 in section...
Part A. Consider the nonlinear equation x5-x=15 Attempt to find a root of this equation with...
Part A. Consider the nonlinear equation x5-x=15 Attempt to find a root of this equation with Newton's method (also known as Newton iteration). Use a starting value of x0=4 and apply Newton's method once to find x1 Enter your answer in the box below correct to four decimal places. Part B. Using the value for x1 obtained in Part A, apply Newton's method again to find x2 Note you should not round x1 when computing x2
Numerical Analysis: Apply the BFGS Method to minimize the function f(x) = x12 - 2x1x2 +...
Numerical Analysis: Apply the BFGS Method to minimize the function f(x) = x12 - 2x1x2 + 4x22 with the starting point x0 = [-3,1]T. Thanks!
the function f(x) = ex - 2e-2x - 3/2 is graphed at right. evidently, f(x) has...
the function f(x) = ex - 2e-2x - 3/2 is graphed at right. evidently, f(x) has a zero in the interval (0,1). (a) show that f(x) is increasing on (-infinity, infinity) (so that no other zero of f exists.) (b) use one iteration of Newton's method to estimate the zero, starting with initial estimate x1 = 0. (c) it appears from the graph that f(x) has an inflection point at or near the zero of f. find the exact coordinates...
Consider a function f(x) = 2x3 − 11.7x2 + 17.7x − 5. Identify the root of...
Consider a function f(x) = 2x3 − 11.7x2 + 17.7x − 5. Identify the root of the given function after the third iteration using the secant method. Use initial guesses x–1 = 3 and x0 = 4. CAN YOU PLZ SHOW ALL THE WORK. THANK YOU
f(x) = ex - 2x - 1 = 0 function's [1; 2] there's a root within...
f(x) = ex - 2x - 1 = 0 function's [1; 2] there's a root within the closed range Show. Graphs f1 (x) = ex and f2 (x) = 2x + 1 functions on an equivalent axis Indicate the situation of the basis by drawing. Functional iteration by taking x0 = 1.5 (sequential approaches) method with 5 decimal precision (5D).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT