Ok this kind of question seems to come up a lot in research and applications but has me completely stumped.(adsbygoogle = window.adsbygoogle || []).push({});

Say we have a dynamical system [tex]x_{t+1} = Ax_t[/tex] where for simplicity we'll assume A is a constantsymmetricreal matrix but otherwise unknown.

1.What is the "best" estimate of A, when only the vectors [tex]x_0[/tex] and [tex]x_1[/tex] are known?

2. What is the new "best" estimate of A when [tex]x_2[/tex] is observed?

Obviously it's ill-posed because there are more unknowns than data. Various generalizations of the problem could include noise, observations of only [tex]y=Bx[/tex], infinite dimensions, etc but question 1 has it in a nutshell.

Any thoughts?

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# Ill-posed inverse problem (linear operator estimation)

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