We want to find the root of the following function using fixed-point iteration: f(x)=2-2ln(x) - x...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
We want to find the root of the following function using fixed-point iteration: f(x)=2-2ln(x) - x a) Finding the root of an equation can be difficult because the algorithm may diverge or go to a different root. One way to help avoid this difficulty is to first graph the function and get an approximation of the root from the graph. Graph the above function and get an estimate of the root from the graph. b) Write a MATLAB script that will implement the fixed-point iteration algorithm to find the root. Use the approximation from (a) as the starting value. Display your root with 10 decimal places. Note: (1) You will need a convergence criteria for (b). Some programs use the machine epsilon for this. For your program, use the machine epsilon. (2) One way to check if your answer is the correct root is to calculate the residual of the answer. The residual is given by substituting your calculated root into the function; this should be very small. In your program, calculate the residual and display it with your root. We want to find the root of the following function using fixed-point iteration: f(x)=2-2ln(x) - x a) Finding the root of an equation can be difficult because the algorithm may diverge or go to a different root. One way to help avoid this difficulty is to first graph the function and get an approximation of the root from the graph. Graph the above function and get an estimate of the root from the graph. b) Write a MATLAB script that will implement the fixed-point iteration algorithm to find the root. Use the approximation from (a) as the starting value. Display your root with 10 decimal places. Note: (1) You will need a convergence criteria for (b). Some programs use the machine epsilon for this. For your program, use the machine epsilon. (2) One way to check if your answer is the correct root is to calculate the residual of the answer. The residual is given by substituting your calculated root into the function; this should be very small. In your program, calculate the residual and display it with your root.
Expert Answer:
Answer rating: 100% (QA)
From the graph we can estimate the root to be around x 05 b Heres a MATLAB script that implements th... View the full answer
Related Book For
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale
Posted Date:
Students also viewed these programming questions
-
Required tool: c program, Linux , pthread_create(), pthread_join(), pthread_attr_setdetachstate(), Suppose you have a doubly link list which each node has a pathname. Write c program to find the...
-
Explain how to derive a sequence of transformations to achieve the overall effect of performing a 2D rotation about an arbitrary point. Discuss the problems of providing tractable models of...
-
What is a function calling convention and how does it impact the design of the RISC-V instruction set architecture (ISA)? [4 marks] (d) Consider the following C function that computes the greatest...
-
Briar Company manufactures and sells dresses at a variable cost of $32 each and a fixed cost of x. It can sell 6,600 dresses at a selling price of $60 to earn an operating income of $14,800 (Option...
-
Go to several fast-food restaurants and develop a value stream map of the operation. Determine whether each restaurant system design achieves the six FRs of system stability.
-
Kellye, Becky, and Emily formed Whoop! Shotz Corporation with the following contributions: Kellye $50,000 cash Becky $50,000 cash Emily Legal services Each was given a...
-
Identify a nursing unit where you know good patient care is given. Discuss what factors in the environment promote the delivery of high-quality patient care. Pay particular attention to how the...
-
Do you believe that one size fits all with respect to corporate governance provisions in different countries around the world? Why or why not? How do legal and cultural factors influence corporate...
-
Actual Manufacturing. In preparation of your DRP and MPS you have learned that the actual amount that can be produced by the design capacity of the production system is actually 600,000 at a time....
-
Question: Find the total deformation energy of the cage in the figure and the vertical displacement of the E point and write only the results in the answer part. B
-
The accountant for Smith, Jones & Webb LLP prepared the following balance sheet immediately prior to liquidation of the partnership: During May 2005, noncash assets with a carrying amount of $105,000...
-
Grossnickle Corporation issued 20-year, noncallable, 9.7% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 7.4%. What is the current...
-
What is the modified internal rate of return (MIRR) of the below project? Answer in the decimal format (e.g. 10.52% is 0.1052) with 4 decimals. If the answer is negative, place a leading hyphen "-"...
-
Nolan Corp. uses no debt. The weighted average cost of capital is 6.7 percent. The current market value of the equity is $28 million and the corporate tax rate is 21 percent. What is the company's...
-
Assume a 10-year Treasury bond has a coupon rate of 3.2 % and par value of $1000, and yield to maturity of 2%. Is this bond selling at a premium or discount? Explain why?
-
At the weekly farmers market in Atlanta, Sean, a local corn farmer, brings a truckload of fresh corn and sells it at a booth. It is more efficient for Sean to produce a large quantity of corn, but...
-
Read this article that describes how the Blake and Mouton Managerial Grid works and provides a test that you can take to see where you fall on the grid. ...
-
This problem continues the Draper Consulting, Inc., situation from Problem 12-45 of Chapter 12. In October, Draper has the following transactions related to its common shares: Oct 1 Draper...
-
Develop, debug, and test a program in either a high-level language or macro language of your choice to generate the transpose of a matrix. Test it on the matrices from Prob. 9.3.
-
Develop a user-friendly program in either a high-level or macro language of your choice for the Gauss-Seidel method based on (Figure). Test your program by duplicating the results of Example 11.3.
-
Use (a) Eulers and (b) The fourth-order RK method to solve dy/dx = -2y + 4e-x dz/dx = -yz2/3 Over the range x = 0 to 1 using a step size of 0.2 with y(0) = 2 and z(0) = 4.
-
Describe the function of a dark pool.
-
Explain the difference between primary and secondary markets.
-
How has the ownership of UK shares changed over the past 50 years?
Study smarter with the SolutionInn App