6-)Find f(x)=(x-2)^3(x-4), accelerate newton iteration numerically sand show that R=2
6-)Find f(x)=(x-2)^3(x-4),
accelerate newton iteration numerically
sand show that R=2
Homework Answers
For the given function
f(x) = (x - 2)^3 *(x - 4)
so,
f'(x) = 3(x - 2)^2(x - 4) + (x - 2)^3
now to find roots we have to put f(x) = 0
from there we can easily see x = 2 and x = 4 are solutions and R =
2 is repeated root
now, from newtons method, let xo = 1
then x1 = xo - f(xo)/f'(xo)
x1 = 1 - (-1)(-3)/(3(-3) + 1) = 1 + 3/8 = 11/8
the following excel sheet has values till x18
| x0 | 1.00000 |
| x1 | 1.30000 |
| x2 | 1.51477 |
| x3 | 1.66663 |
| x4 | 1.77270 |
| x5 | 1.84598 |
| x6 | 1.89612 |
| x7 | 1.93019 |
| x8 | 1.95320 |
| x9 | 1.96868 |
| x10 | 1.97907 |
| x11 | 1.98602 |
| x12 | 1.99067 |
| x13 | 1.99378 |
| x14 | 1.99585 |
| x15 | 1.99723 |
| x16 | 1.99815 |
| x17 | 1.99877 |
| x18 |
1.99918 |
taking initial value 3 gives us
| x0 | 3.00000 |
| x1 | 2.50000 |
| x2 | 2.31250 |
| x3 | 2.20148 |
| x4 | 2.13172 |
| x5 | 2.08675 |
| x6 | 2.05739 |
| x7 | 2.03807 |
| x8 | 2.02530 |
| x9 | 2.01683 |
| x10 | 2.01120 |
| x11 | 2.00746 |
| x12 | 2.00497 |
| x13 | 2.00331 |
| x14 | 2.00221 |
| x15 | 2.00147 |
| x16 | 2.00098 |
| x17 | 2.00065 |
| x18 | 2.00044 |
using initial value 3.5 gives us division by 0 error, using 3.6 gives
| x0 | 3.60000 |
| x1 | 5.20000 |
| x2 | 4.63529 |
| x3 | 4.26663 |
| x4 | 4.06955 |
| x5 | 4.00637 |
| x6 | 4.00006 |
| x7 | 4.00000 |
| x8 | 4.00000 |
| x9 | 4.00000 |
| x10 | 4.00000 |
| x11 | 4.00000 |
| x12 | 4.00000 |
| x13 | 4.00000 |
| x14 | 4.00000 |
| x15 | 4.00000 |
| x16 | 4.00000 |
| x17 | 4.00000 |
| x18 | 4.00000 |
hence we can see, R = 2, is repeated root and E = 4 is single root
Add Answer to:
6-)Find f(x)=(x-2)^3(x-4),
accelerate newton iteration numerically
sand show that R=2
OD Find the multiplicity of the root f(x)= (x-3) in (x-2) 162) Find the order of...
OD Find the multiplicity of the root f(x)= (x-3) in (x-2) 162) Find the order of convergence (prove that R=3) for loon 03) FLO) = X3 - 2-3 a digits accuracy ** 14) Find RA for both roots theoretically and numerically: f(x) = (x-2)} (x-4) 65) Estimate the root R and A both theoretically and - numerically f(x) = x²-340SX-7 06) Use Accelerated Neuston iteration and show that 2=2 elemele de F(X) = (x-2) 3 CX-4) - 07) Estimate the...
6) Use MATLAB and Newton-Raphson method to find the roots of the function, f(x) = x-exp...
6) Use MATLAB and Newton-Raphson method to find the roots of the function, f(x) = x-exp (0.5x) and define the function as well as its derivative like so, fa@(x)x^2-exp(.5%), f primea@(x) 2*x-.5*x"exp(.5%) For each iteration, keep the x values and use 3 initial values between -10 & 10 to find more than one root. Plot each function for x with respect to the iteration #.
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3...
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling?
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling?
4. Use Newton Method to find the approximate solutions of the equations. Stop your iteration when...
4. Use Newton Method to find the approximate solutions of the equations. Stop your iteration when **+1 - <0.01. (a) x -2-5=0, (1,4) (b) e' - 32 0 , 0,1 5. Use Newton Method to compute the approximate solutions 24 and is of the equation
2. (a) We want to find the root x of the function f(x); that is, we need f(r) = 0 . This can be done using Newton...
2. (a) We want to find the root x of the function f(x); that is, we need f(r) = 0 . This can be done using Newton's method, making use of the iterative formula f(xn) Show that the sequence ofiterates (%) converges quadratically if f'(x) 0 in some appropriate interval of x-values near the root χ 9 point b) We can get Newton's method to find the k-th root of some number a by making it solve the non-linear cquation...
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print ...
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print the iterative steps. Use a) Fixed Point Iteration and b) Newton Raphson. The initial values and the convergence criteria are up to you.
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print the...
Predict the roots of the polynomial f(x)=x^3-6x^2+11x-6 writing a code. Show your code and print the iterative steps. Use a) Fixed Point Iteration and b) Newton Raphson. The initial values and the convergence criteria are up to you.
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1...
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1 Use an initial guess of xo = 1.2 and perform 3 iterations. For the N-R method: Xi+1 = x; - f(x;) f'(x;)
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6?...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6? + 10 a. Write a Python function for the derivative of f(x) that takes x and returns the derivative of f(x). Take the derivative of f(x) analytically with respect to x before writing the function. b. Write a Python code that approximately finds the real root, x0, of f(x) such that f(x0)~0 using the Newton-Raphson method. The code is expected to get an initial...
3 Newton and Secant Method [30 pts]. We want to solve the equation f(x) 0, where f(x) = (x-1 )4. ...
Can you help me with parts A to D please? Thanks
3 Newton and Secant Method [30 pts]. We want to solve the equation f(x) 0, where f(x) = (x-1 )4. a) Write down Newton's iteration for solving f(x) 0. b) For the starting value xo 2, compute x c) What is the root ξ of f, i.e., f(5) = 0? Do you expect linear or quadratic order of convergence to 5 and why? d) Name one advantage of Newton's...
OD Find the multiplicity of the root f(x)= (x-3) in (x-2) 162) Find the order of convergence (prove that R=3) for loon 03) FLO) = X3 - 2-3 a digits accuracy ** 14) Find RA for both roots theoretically and numerically: f(x) = (x-2)} (x-4) 65) Estimate the root R and A both theoretically and - numerically f(x) = x²-340SX-7 06) Use Accelerated Neuston iteration and show that 2=2 elemele de F(X) = (x-2) 3 CX-4) - 07) Estimate the...
6) Use MATLAB and Newton-Raphson method to find the roots of the function, f(x) = x-exp (0.5x) and define the function as well as its derivative like so, fa@(x)x^2-exp(.5%), f primea@(x) 2*x-.5*x"exp(.5%) For each iteration, keep the x values and use 3 initial values between -10 & 10 to find more than one root. Plot each function for x with respect to the iteration #.
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling?
3. Find all fixed points for the associated Newton iteration function for F(a) z/ 1) when n-1,2,3... Which are attracting and which are repelling?
4. Use Newton Method to find the approximate solutions of the equations. Stop your iteration when **+1 - <0.01. (a) x -2-5=0, (1,4) (b) e' - 32 0 , 0,1 5. Use Newton Method to compute the approximate solutions 24 and is of the equation
2. (a) We want to find the root x of the function f(x); that is, we need f(r) = 0 . This can be done using Newton's method, making use of the iterative formula f(xn) Show that the sequence ofiterates (%) converges quadratically if f'(x) 0 in some appropriate interval of x-values near the root χ 9 point b) We can get Newton's method to find the k-th root of some number a by making it solve the non-linear cquation...
Use the Newton-Raphson method to find the root of f(x) = e-*(6 - 2x) - 1 Use an initial guess of xo = 1.2 and perform 3 iterations. For the N-R method: Xi+1 = x; - f(x;) f'(x;)
Can you help me with parts A to D please? Thanks
3 Newton and Secant Method [30 pts]. We want to solve the equation f(x) 0, where f(x) = (x-1 )4. a) Write down Newton's iteration for solving f(x) 0. b) For the starting value xo 2, compute x c) What is the root ξ of f, i.e., f(5) = 0? Do you expect linear or quadratic order of convergence to 5 and why? d) Name one advantage of Newton's...
Most questions answered within 3 hours.
-
Do not neglect the old for the new. The existing business must
not lose priority simply...
asked 2 hours ago -
Kylie is a single mom with two dependent children,
Tanner, age 7 and Olivia, age 11....
asked 3 hours ago -
Phosphorous + bromine = phosphorous tribromide. If 35.0 g of
bromine are reacted and 27.9 grams...
asked 5 hours ago -
Derive the long wavelength limit of the Planck energy density
distribution
asked 5 hours ago -
Calculate the pH of each of the following solutions.
0.50 M HBr
3.1×10−4 M KOH
4.2×10−5...
asked 8 hours ago -
For the year ended December 31, Depot Max’s cost of merchandise
sold was $85,600. Inventory at the...
asked 8 hours ago -
Week 10 - Professional Memo Assignment
Professional Memo Assignment
Your mission for this week, should you...
asked 8 hours ago -
Write a Python program that stores the data for each
player on the team, and it...
asked 9 hours ago -
In
the last 3 months, mike never knows when he is going to get his
allowance...
asked 9 hours ago -
Is Ca(OH)2 a Bronsted base, Lewis base, or both? Why?
asked 9 hours ago -
1A- Why don’t voters complain about U.S. tariffs on imported
sugar?
Because sugar is only a...
asked 9 hours ago -
Cash Payback Period
Primera Banco is evaluating two capital investment proposals for
a drive-up ATM kiosk,...
asked 9 hours ago