modified newton raphson in matlab

To modify the Newton-Raphson method in Matlab, you need to implement the changes according to your specific needs. Here's the basic syntax of the standard Newton-Raphson method in Matlab:

main.m
function [root,ea,iter]=newtraph(f,xr,es,maxit)
%newtraph: Newton-Raphson root location zeroes
%  [root,ea,iter]=newtraph(func,xr,es,maxit): uses the Newton-Raphson
%  method to find the root of func
% input:
%   func = name of function
%   xr = initial guess
%   es = desired relative error (default = 0.0001%)
%   maxit = maximum allowable iterations (default = 50)
% output:
%   root = real root
%   ea = approximate relative error (%)
%   iter = number of iterations
...

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From here you can make any necessary changes. For example, you can add a parameter to adjust the damping factor to ensure convergence. Or, you can add a condition to terminate the function after a certain number of iterations to prevent an endless loop.

Here's an example of how to modify the damping factor:

main.m
function [root,ea,iter]=newtraph(f,xr,es,maxit,damping_factor)
%newtraph: Newton-Raphson root location zeroes
%  [root,ea,iter]=newtraph(func,xr,es,maxit,damping_factor): uses the
%  damped Newton-Raphson method to find the root of func
% input:
%   func = name of function
%   xr = initial guess
%   es = desired relative error (default = 0.0001%)
%   maxit = maximum allowable iterations (default = 50)
%   damping_factor = damping factor for the damped Newton-Raphson method
% output:
%   root = real root
%   ea = approximate relative error (%)
%   iter = number of iterations
...

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Then, you can implement the changes in the function.

You can also modify the method to use a hybrid method, where it switches to another numerical method if the Newton-Raphson method doesn't converge.

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