Changing stop criteria for vpasolve

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Sayed am 2 Sep. 2014

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https://de.mathworks.com/matlabcentral/answers/153213-changing-stop-criteria-for-vpasolve

Bearbeitet: Sayed am 3 Sep. 2014

What is the stop criteria for " vpasolve" and how can I change it? If changing is not possible for vpasolve, please let me know if there is any other command for numerical solving of a "set of nonlinear equations" that I can change its stopping criteria (e.g. error<1e-10)

Why am I looking for this?! 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 & 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 they vary in each experiment. I can only determine them through my measurement system. So, I should change the solving method (or may be its sensitivity) for the above eqs. set in order to give me the answer even by non-exact LHS values. Please let me know what should I do in this case. Thanks

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José-Luis am 2 Sep. 2014

I am not sure I understand, but aren't you trying to solve the problem backwards? What you could do is do a regression analysis to find the parameters and look at the their confidence interval, or regression error. If the "true" values are within this interval, then the variation would be within measurement error.

Sayed am 2 Sep. 2014