# implement the secant method with x0 = 0.5, x1 = 0.6, and |xk −xk−1|

< 10−10 as a convergence criteria. Find the root of f(x) = x + ln(x) for x> 0. I was kinda stuck on finding the ratio of the error.

function [x errors rate] = secant(x0,x1,f,atol)

% x0, x1 initial values

x0 = 0.5;

x1 = 0.6;

% f function

f = @(x) x+ log(x);

% atol |x_{k}-x_{k-1} <= atol

atol = 1e-10;

% x: root, so that f(x) = 0

% error: used to measure convergence |x_{k}-x_{k-1}

% rate: ratio of errors e_{k+1}/e_k

max_iter = 500;

count = 0;

errors = x1-x0; % fill in this row array

rate = ; % fill in this row array

while(count < max_iter) && errors > 1e-10 % add additional stopping criteria here

count = count+1;

fx0 = f(x0);

fx1 = f(x1);

x2 = x1+f(x1)*(x1-x0)/f(x1)-f(x0); % fill this in with the secant formula

errors(count) = x1 - x0; % fill this in with |x_k - x_{k-1}|

end

x = x2;

rate = errors(2)/errors(1); % fill in this array with errors(k+1)/errors(k);

end

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