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//Example 2.2
clc
clear
function [root] = FalsePosition(fun,x,tol,maxit)
// FalsePosition: Computes roots of the function in the given range using False Position Method
//// Input: FalsePosition(fun,x,tol,maxit)
// fun = function handle
// x = range in between sign change is evident
// tol = Maximum error between iterations that can be tolerated
// maxit = Maximum number of iterations
//// Output: [root]
// Root: Root of the given function in defined range
if fun(x(1)) > 0 then
xu = x(1); xl = x(2);
else
xu = x(2); xl = x(1);
end
Ea = 1;
iter = 1;
while(1)
xr(iter) = xl(iter) - ((xu(iter)-xl(iter)) / (fun(xu(iter))-fun(xl(iter))) * fun(xl(iter)));
if fun(xr(iter)) > 0 then
xu(iter+1) = xr(iter);
xl(iter+1) = xl(iter);
elseif fun(xr(iter)) < 0 then
xl(iter+1) = xr(iter);
xu(iter+1) = xu(iter);
else
break
end
if iter>1 then
Ea(iter) = 100 * abs((xr(iter) - xr(iter-1)) / xr(iter));
end
if Ea(iter) < tol | iter == maxit then
break
end
iter = iter + 1;
end
root = xr(iter);
endfunction
function f = fun1(x)
f = x.^3 -9*x + 1;
endfunction
x = [2 4; 2 3];
tol = 1e-4;
maxit = 3;
for i = 1:2
root = FalsePosition(fun1,x(i,:),tol,maxit);
root = round(root*10^5)/10^5;
disp(strcat(["root(",string(i),") = ",string(root)]))
end
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