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If the solution were a smooth function, one could carry out a Taylor expansion, which is a way of approximating the function by polynomials of increasingly higher degree.
At graphical resolution, very similar fits to the discrete functions are provided by polynomials of order 7 and above.
In the theory model, the spring and the damper are represented by polynomial functions of the relative displacement.
Portions of the methodology can also be used for the optimal approximation, by piecewise linear polynomials, of given functions containing discontinuities.
We consider a SIMO system with two outputs represented by polynomial transfer function of degree L = 66.
Then the model's parameters are identified by the non-linear least square method from test data and fitted by the polynomials as functions of the supplied current.
Our method consists of reducing the given weakly singular integral equation to a set of algebraic system by expanding the unknown function by Chebyshev polynomials of the first kind.
To solve above problems, the original ESN is extended to polynomial ESNs (PESNs) by employing the polynomial functions of input variables into output weights.
As the version of Go without modification (ii) can be shown to be \ \textbf{EXP}\ -complete (Robson 1983), the fact that GO as described above is in \ \textbf{EXP}\ -completes on the fact that the length of any legal sequence of moves is bounded by a polynomial function of the size of the input boaRobsonition.
The severe errors associated with the computation of derivatives of functions approximated by Chebyshev polynomials are investigated.
The mean diameter and coefficient of variation were modeled by polynomial response surfaces as functions of solution concentration and voltage at each collector distance.
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