# Can we solve can overdetermined coupled equations in matlab?

for k=1:len
thetaHattt(k)=atan(((Ahat+Rhat)*(1/k11(k)*Bhat-Chat)+Ahat*(Chat-1/k22(k)*Bhat))/((1/k22(k)*(Ahat+Rhat)*(1/k11(k)*Bhat-Chat)+1/k11(k)*Ahat*(Chat-1/k22(k)*Bhat))));
if k<len&&k>1
chatt(k)=Ahat/(k11(k-1)-k11(k))*(sin(thetaHattt(k-1))-sin(thetaHattt(k))-k11(k-1)*cos(thetaHattt(k-1))+k11(k)*cos(thetaHattt(k)));
Ahatt(k)=(k11(k-1)-k11(k))*chatt(k)/((sin(thetaHattt(k-1))-sin(thetaHattt(k))-k11(k-1)*cos(thetaHattt(k-1))+k11(k)*cos(thetaHattt(k))));
Bhatt(k)=k11(k)*(chatt(k)+Ahatt(k)*cos(thetaHattt(k)))-Ahatt(k)*sin(thetaHattt(k));
Rhatt(k)=(k22(k)*chatt(k)+k22(k)*Ahatt(k)*cos(thetaHattt(k))-Bhatt(k)-Ahatt(k)*sin(thetaHattt(k)))/(sin(thetaHattt(k))-k22(k)*cos(thetaHattt(k)));
end
end


In the above code,there are 5 unknowns Ahat,Bhat,Chat, Rhat and thetaHattt. All the five equations are given. K11 and K22 are vectors of length 10 and are known. The question is with the known K11 and K22 can we somhow find the values of the 5 unknowns given the constraint equations as above. chatt is same as Chat, Ahatt is same as Ahat. I am giving different variables just to show the equations. Any comment please.

Edit: One can further put a constraint that rate of change of thetaHatt with respect to the variable (k) is constant.

• It would help if you could write your equations in standard mathematical notation using Latex/Mathjax, so that they are more readable. – Federico Poloni Jun 18 at 7:25