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Newton's method is the classic algorithm for finding roots of functions. The breif introduction is written below.
The analytic solution is
The code isclear all
x = zeros(1,2);
f = zeros(1,2);
tol = 1E-7;
invJ = zeros(2,2);
x(1) = 0.23;
x(2) = 0.69;
for n = 1:1:1E4
f(1) = x(1)+85.4/x(2)-1;
f(2) = x(1)-10/x(2);
invJ(1,1) = 10/95.4;
invJ(1,2) = 85.4/95.4;
invJ(2,1) = -x(2)^2/95.4;
invJ(2,2) = x(2)^2/95.4;
xn = x'-invJ*f';
if (abs(x(1)-xn(1))/abs(xn(1)) < tol ...
&& abs(x(2)-xn(2))/abs(xn(2)) < tol)
fprintf('The maximum number of iterations is %d\n', n)
disp('The solution within tolerance 1E-7 is')
disp(xn')
return;
end
x = xn';
end
disp('The solution did not converge to x-axis')
The generated result is
