I have been using the Trust-Region Dogleg Method in MATLAB to solve a system of nonlinear equations: f(x)=c. However, when I change the values of the c vector to certain values, MATLAB returns that the problem is locally singular. When I outpu the jacobian, the determinant is about 1, so this matrix is not singular. Is is possible to have a locally singular equation without a singular jacobian?
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I have seen in the past that MATLAB gives this warning if you require extremely high accuracy (low tolerance). What are your tolerances? Can you give more info?
I apologize I didn't post this as a comment, but I don't have commenting privilleges yet. And I couldn't reach you via profile.

Ludi
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