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Cantvector, should accept the following inputs to a MATLAB function of the form y = fun(x) that returns fox, the root finding funcfion 2 infial guesses for the root relative error for the root given by (note that thia is not e percentoge in this case) um number of iterations un the following output ll of the computed root estimates (assume that the firet two root estimates for the output vector, x, are the two intial values contained in xe the following Secant method by retaining each root estmate. Donatusa the MATLAR siver tunctions like fzere salve costs ets alues for the stopping eror (0.001) and the maximum number of terations (50) if they have not been passed as parameters. This can be done using the nargin command. If the number of arguments passed in is less than 5, detin earch when the reiative error tolerance is reached or when the iteration imt is reached (whichever occurs first). oes not converge before the iteration limt is reached. set i= Nan and use the MATLAB function warning with a message : 1terationsinitexceeded am answer the following at the end of your code: ue be preferatle to the original secant method code written in the activities?

Cantvector, should accept the following inputs to a MATLAB function of the form y = fun(x) that returns fox, the root finding funcfion 2 infial guesses for the root relative error for the root given by (note that thia is not e percentoge in this case) um number of iterations un the following output ll of the computed root estimates (assume that the firet two root estimates for the output vector, x, are the two intial values contained in xe the following Secant method by retaining each root estmate. Donatusa the MATLAR siver tunctions like fzere salve costs ets alues for the stopping eror (0.001) and the maximum number of terations (50) if they have not been passed as parameters. This can be done using the nargin command. If the number of arguments passed in is less than 5, detin earch when the reiative error tolerance is reached or when the iteration imt is reached (whichever occurs first). oes not converge before the iteration limt is reached. set i= Nan and use the MATLAB function warning with a message : 1terationsinitexceeded am answer the following at the end of your code: ue be preferatle to the original secant method code written in the activities?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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The Secant method is an open method for root finding that requires two intial values (which do not need to bracket the root). In the activities, you wrote a code which performed the secant method without saving the previous root values using the following iteration algorithm: Rewrite the secant method code, so that you save each new root in a vector x. The iteration algorithm can be rewritten like this: - Your function, called secantvector, should accept the following inputs • fun = a handle to a MATLAB function of the form y = fun(x) that returns f(x), the root finding function, • xe = a vector of 2 initial guesses for the root • Tolx - desired relative error for the root given by (note that this is not a percentage in this case) . itmax = maximum number of iterations Your function should return the following output: • x= a vector of all of the computed root estimates (assume that the first two root estimates for the output vector, x, are the two initial values contained in xe) Your solution should do the following 1. Implement the Secant method by retaining each root estimate. Do not use the MATLAB solver functions like fzere solve coots etc. 2. Define default values for the stopping error (0.001) and the maximum number of iterations (50) if they have not been passed as parameters. This can be done using the nargin command. If the number of arguments passed in is less than 5, define maxit and if it is less than 4 define both maxit and es within the function. 3. Terminate the search when the relative error tolerance is reached or when the iteration limit is reached (whichever occurs first). 4. If the iteration does not converge before the iteration limit is reached, set i = Nan and use the MATLAB function warning with a message : 'IterationLimitExceeded' After writing the program answer the following at the end of your code: When would this technique be preferable to the original secant method code written in the activities? Function e C Reset E MATLAB Documentation 1 function [x] = secantvector(f,xest,es,maxit) 2 % uses the Secant method to find the root 3% of the function f, and returns a vector x with all of the root estimate iterations 4
Transcribed Image Text:The Secant method is an open method for root finding that requires two intial values (which do not need to bracket the root). In the activities, you wrote a code which performed the secant method without saving the previous root values using the following iteration algorithm: Rewrite the secant method code, so that you save each new root in a vector x. The iteration algorithm can be rewritten like this: - Your function, called secantvector, should accept the following inputs • fun = a handle to a MATLAB function of the form y = fun(x) that returns f(x), the root finding function, • xe = a vector of 2 initial guesses for the root • Tolx - desired relative error for the root given by (note that this is not a percentage in this case) . itmax = maximum number of iterations Your function should return the following output: • x= a vector of all of the computed root estimates (assume that the first two root estimates for the output vector, x, are the two initial values contained in xe) Your solution should do the following 1. Implement the Secant method by retaining each root estimate. Do not use the MATLAB solver functions like fzere solve coots etc. 2. Define default values for the stopping error (0.001) and the maximum number of iterations (50) if they have not been passed as parameters. This can be done using the nargin command. If the number of arguments passed in is less than 5, define maxit and if it is less than 4 define both maxit and es within the function. 3. Terminate the search when the relative error tolerance is reached or when the iteration limit is reached (whichever occurs first). 4. If the iteration does not converge before the iteration limit is reached, set i = Nan and use the MATLAB function warning with a message : 'IterationLimitExceeded' After writing the program answer the following at the end of your code: When would this technique be preferable to the original secant method code written in the activities? Function e C Reset E MATLAB Documentation 1 function [x] = secantvector(f,xest,es,maxit) 2 % uses the Secant method to find the root 3% of the function f, and returns a vector x with all of the root estimate iterations 4
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