Polynomials, evaluating using array

Evaluating polynomials or power Series USING Array formulas... 

The stationary state of the network of reactors is stable, if all roots A, of (13.8) have a negative real part. The necessary and sufficient conditions for this to hold are the Routh-Hurwitz conditions, see Theorem 1.2. The stationary state of the network, W, undergoes a stationary instability if = 0, see (1.36), and an oscillatory instability if = 0, together with > 0, A > 0, Z = 1,..., m — 2, see (1.38). The Routh-Hurwitz analysis can be used to determine, in principle, the stability properties of the steady state of any network, even inhomogeneous networks. This advantage is, however, balanced by the fact that it is a computationally expensive task to evaluate all the coefficients C of the characteristic polynomial and the Hurwitz determinants A . In our studies of instabilities in arrays of coupled reactors, we used symbolic computation software, namely Mathematica (Wolfram Research, Inc., Champaign, IL, 2002) and Maple (Waterloo Maple Inc., Waterloo, Ontario, 2002), to obtain exact, analytical expressions for the coefficients C of the characteristic polynomial (13.8) and the Hurwitz determinants A/ for arrays of up to six coupled reactors. 

Function-based methods choose a particular function (like a polynomial) and determine coefficients to make one or more functions pass through the input pixels. Afterwards, the functions are used to create a regular voxel array by evaluating the functions at regular intervals. 

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