We want to find the root of the following function using fixed-point iteration: f(x)=2-2ln(x) - x...

 

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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.

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The question provides a function fx 2 2lnx sqrtx and asks to find its root using fixedpoint iteratio... View the full answer