Recursion elimination

Another reason for non-recursive non-minimal cases is recursion elimination by partial evaluation. The result is a non-minimal case that looks like a minimal case. This is hard to detect, since the cases still exhibit mutually exclusive structural forms. There is no limit to creating non-recursive non-minimal cases by partial evaluation. 

When both G12 = G21 = 0, the system is decoupled and behaves identically to two single loops. When either G12 = 0 or G21 = 0, the situation is referred to as one-way interaction, which is sufficient to eliminate recursive interactions between the two loops. In such a case, one of the loops is not affected by the second while it becomes a source of disturbance to this second loop. 

Niedzwiecki, 1994] Niedzwiecki, M. (1994). Recursive algorithm for elimination of measurement noise and impulsive disturbances from ARMA signals. Signal Processing VII Theories and Applications, pages 1289-1292. 

Equations (5-42) to (5-44) constitute a set of simultaneous linear equations in the unknown values of the quantity on the new profile, each of the sets for temperature and the conversions being independent. The matrix of coefficients is the same for each conversion, and differs for the temperature only in one element, the one containing the heat-transfer coefficient. An important property of each matrix of coefficients is that it is independent of the axial position, so that for the purpose of the calculation it is a constant matrix. Another important property is that only three diagonals of the matrix contain elements that are not zero. These properties make it possible to throw the calculation of the unknown quantities into a very simple form. The essential feature of the calculation is that coefficients in two two-term recursion formulas are constructed from the matrix elements, and then these coefficients are used to calculate, first, a set of ancillary quantities, and then the desired quantities. The procedure is exactly what would be used in eliminating the unknown quantities successively from the equations and then sub-... 

By successively eliminating the Q functions, this gives a general equation in recursive fonu as before ... 

The effects of autocorrelation on monitoring charts have also been reported by other researchers for Shewhart [186] and CUSUM [343, 6] charts. Modification of the control limits of monitoring charts by assuming that the process can be represented by an autoregressive time series model (see Section 4.4 for terminology) of order 1 or 2, and use of recursive Kalman filter techniques for eliminating autocorrelation from process data have also been proposed... 

It is frequently effective to use block representation of parallel algorithms. For instance, a parallel version of the nested dissection algorithm of Section VIII.C for a symmetric positive-definite matrix A may rely on the following recursive factorization of the matrix Ao = PAP, where P is the permutation matrix that defines the elimination order (compare Sections III.G-I) ... 

The Newton-Euler method is well suited to a recursive formulation of the kinematic and dynamic equations of motion (Pandy and Berme, 1988) however, its main disadvantage is that all of the intersegmental forces must be eliminated before the governing equations of motion can be formed. In an dtemative formulation of the dynamical equations of motion, Kane s method (Kane and Levinson, 1985), which is also referred to as Lagrange s form of D Alembert s principle, makes explicit use of the fact that constraint forces do not contribute directly to the governing equations of motion. It has been shown that Kane s formulation of the dynamical equations of motion is computationally more efficient than its counterpart, the Newton-Euler method (Kane and Levinson, 1983). 

It has been shown in this study how the elimination of irrelevant paths from moment diagrams contributes to an enhanced understanding of the pertinent terms (first the chain parameters, then the eigenvalues and residues) which determine the dynamics. Due to conservation of the orthogonality of the recursive states with respect to the source state, assured by the present diagrammatic moment procedure, satisfactory convergence of the numerical results is shown and the contribution of numerical round-off errors is suppressed. 

The construction of an AH is conducted in a recursive and bottom-up manner, where it starts from the lowest level of detail (level zero) and subsequently building higher levels based on the abstract class accessibility relationships that exist among different AECs. The layering process is designed to eliminate backtracking in the plan. 

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