I have a set of nonlinear equations which are related to a physical system. The constants of these equations (light hand side values-LHS) are determined through some measurement methods. It means that the determined constants will not be 100% accurate and so when I solve the equation set through Matlab, I cannot get any answer! For example in one experiment, ideally I should have the following eqs: (X, Y and Z are my constants and a & b are my unknowns)
syms a1 a2 a3 b1 b2 b3
X1=2/3;
X2=5/3;
X3=2/3;
Y1=5/2;
Y2=1/2;
Y3=1/2;
Z1=2;
Z2=1;
Z3=0;
S = vpasolve([X1==b1-b2*b3/a1,X2==a2-b3^2/a1,X3==a3-b2^2/a1,Y1==a1-b3^2/a2,Y2==b2-b1*b3/a2,Y3==a3-b1^2/a2,Z1==a1-b2^2/a3,Z2==a2-b1^2/a3,Z3==b3-b1*b2/a3], [a1, a2, a3, b1, b2, b3])
Solving with Matlab, it returns: a1=3, a2=2, a3=1, b1=1, b2=1, b3=1. But, when I get the constant LHS's through my measurement system, each one is a bit less than or greater than the corresponding exact value (e.g. in the above eqs set just consider Y2=0.499 instead of 0.5) and so Matlab cannot solve the equation set any more and returns no answer. Please be advised that I do not know the exact values of my constants and I can only determine them through my measurement system and they vary in each experiment. So, I should change the solving method (or may be its sensitivity) for the above eqs. set in order to be able to give me an answer in case of having non-exact LHS values. Please let me know what would be better to do in this case. Thanks