- #1

bpet

- 532

- 7

Ok this kind of question seems to come up a lot in research and applications but has me completely stumped.

Say we have a dynamical system [tex]x_{t+1} = Ax_t[/tex] where for simplicity we'll assume A is a constant

1.

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?

Say we have a dynamical system [tex]x_{t+1} = Ax_t[/tex] where for simplicity we'll assume A is a constant

**symmetric**real 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?

Last edited: