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MATLAB: Create a function that will use the Secant method to try to find a root by modifying the False Position method function written bellow. Because this method may diverge, you should limit the number of time the loop repeats.
function [fproot,zeroerror] = falsepos(func, low, high, accepterror)% function to find the root of an equation using false position method and% two guesses.% input: function, low value for a guess, high value for a guess, and% acceptable error for root.% output: The root or an empty matrixif the root is not found.% processing: Find a possibility for the root by creating a line between% low value high value. New possibility is where the line% intersects the x-axis. New possibility may be calculated by% the equation% xnew = xhigh - ((f(xhigh)(xlow -xhigh))/(f(xlow) - f(xhigh))% Then f(xnew) will be calculated. If f(xnew) is equal to 0,% set root to xnew and set logical variable to false.% Otherwise compare the sign of f(xnew) is the same as the% sign of low. If it the same, then set low to xnew,% set high to xnew. Repeat until root is found or difference% between xlow and xhigh is less than 0.0000001.
notfound = true;diff = abs(high - low);fproot =[];while (notfound & diff > 0.00000001 )flow = func(low);fhigh = func(high);xnew = high - ((fhigh)*(low - high))/(flow - fhigh);fnew = func(xnew);if abs(fnew) < accepterrorfproot = xnew;notfound = false;zeroerror = fnew;elseif sign(fnew) == sign(flow)low = xnew;elsehigh = xnew;enddiff = abs(high - low);
end
if notfounddisp('No roots were found in this range!')disp('Try again with new guesses')end
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