matlab secant method

% Matlab script to illustrate the secant method
% to solve a nonlinear equation


% this particular script finds the square root of a number M
% (input by the user)


% note that the function we are trying to zero is f(x) = x^2 - M.
% this function is hard-coded in the script.




g=9.8065;
k=0.00341;
% f(x)=log(cosh(t*srt(g*k)))/k;




format long


% get user input
M = input(‘Please enter the number whose square root you want: ‘)
t0 = input(‘Please enter the first  of two starting guesses: ‘)
t1 = input(‘Please enter the second of two starting guesses: ‘)




% iteration counter
k = 1
% compute first secant iterate to enter loop
s = (((log(cosh(t1*sqrt(g*k)))/k)-M)-((log(cosh(t0*sqrt(g*k)))/k)-M) )/(t1-t0);
% s = ( (x1^2-M) - (x0^2-M) ) / (x1 - x0);
t = t1 - (((log(cosh(t1*sqrt(g*k)))/k)-M))/s
% x = x1 - (x1^2-M)/s
disp(‘Hit return to continue‘)
pause 


while abs(t-t1) > eps*abs(t),
    % reset guesses
    t0 = t1;
    t1 = t;
    % increment iteration counter
    k = k + 1
    % compute and display secant iterate
    s = (((log(cosh(t1*sqrt(g*k)))/k)-M)-((log(cosh(t0*sqrt(g*k)))/k)-M) )/(t1-t0);
%     s = ( (x1^2-M) - (x0^2-M) ) / (x1 - x0);
%     x = x1 - (x1^2-M)/s
    t = t1 - (((log(cosh(t1*sqrt(g*k)))/k)-M))/s
    disp(‘Hit return to continue‘)
    pause 
end