Not really. Gershgorin's circle theorem says you must be close but not how close usually. I would try to get a plot of your data and pick an easy to determine point that is pretty close to where your solution should be. Good luck, David Booth Remember if one choice doesn't work try another. I would try several choices anyway to make sure the solution is stable. Hopefully I understood your question.

Safa gave very good advice. Best, David Booth

Thanks Dear Prof. Booth

As I understand from your answer, the only possibility is to determine the border of the estimation of unknown parameters. But it could not be verified to reach to the global minimum by selecting the initial values inside the Gershgorin's circle, and it would be possible to be trapped in local minimums.

Am I right?

Dear Safa Aouinti

Thank you too for your guide.

According to the link you mentioned, there is no universal approach to set the initial values in order to be sure to get to the global minimum, unless general considerations like noticing to the graphical features of the diagram or estimating the parameters one by one.

How about the algorithms like Marqurdt's one that using hybrid optimizations? Is there any algorithm to be less sensitive to initial values and also to be fast or at least not slow so much?

Well, generally not even that. Inside the circle the algorithm converges. The radius is called the radius of convergence. But for most examples the calculation of such things is an unsolved problem. If you are interested in following this thread I would consult a numerical analyst. I believe the local minimum problem is also unsolved. I admit to being out of my depth at this point. Best wishes, David Booth

Dear prof. Booth

It is very thankful devoting your time to answer my questions.

Getting a consultation will be of great pleasure, ofcourse provided that it does not disturb you!