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Deductions of the energy function

For time series prediction I can rewrite the prediction problem in a standard Energy-minimization form. I used a Lyapunovgif based development of an energy function, with weights' change, therefore matrix derivation.

In order to achieve a more robust representation, I developed a new energy function by applying the standard quadratic penalties to the newly constructed restriction inequalities, and obtained:

  eqnarray135

with tex2html_wrap_inline1442 constants. Equation 2 states that the energy of the system depends only on the maximum error radius tex2html_wrap_inline1444 , as long as the restrictions are satisfied. If not, the terms tex2html_wrap_inline1446 , tex2html_wrap_inline1448 also contribute to the error function.

The basic idea of this approach is that tex2html_wrap_inline1444 not only controls all the other errors, but also ensures convergence by decreasing monotonously. If the maximum error(ME) radius decreases, so will all other errors contained in the error sphere. Which is more, the decreasing step is set by the decreasing step of the ME, that can be adjusted in order to assure convergence.



Alexandra Cristea
Tue Feb 9 20:20:27 JST 1999