Recursive coupling

Jones-Hertzog DK, Mukhopadhyay P, Keefer CE, Young SS. Use of recursive partitioning in the sequential screening of G-protein-coupled receptors. J Pharmacol Toxicol 2000 10 207-15. 

Bodenhausen ° developed a pattern-recognition programme (MARCO POLO) in order to extract coupling pathways in COSY spectra. He subsequently described a recursive deconvolution technique for the measurement of couplings, but this seems to offer more benefits to the measurement of scalar couplings in two-dimensional spectra than in one-dimensional spectra. 

Based on a perturbation expansion using the KS Hamiltonian [26,27], recently a new systematic scheme for the derivation of orbital-dependent Ec has been proposed [12]. While this representation is exact in principle, an explicit evaluation requires the solution of a highly nonlinear equation, coupling Exc and the corresponding x>xc [19]. For a rigorous treatment of this Exc one thus has to resort to an expansion in powers of e, which allows to establish a recursive procedure for the evaluation of Exc and the accompanying Vxc-... 

Moore [Moore, 1977b] studied the effect of oscillator implementation using lookup tables and found that linear interpolation produces the least distortion and that truncation produces the worst. This result was confirmed by Hartmann [Hartmann, 1987], Another possibility is to use a recursive (HR) filter with poles located on the unit circle. This coupled form [Tierney et al., 1971] offers a alternate method that avoids using memoiy space. Frequency resolution requirements were calculated by Snell in a superpipeline oscillator design for dynamic Fourier synthesis [Snell, 1977]. 

Based on current knowledge of the process and its disturbance characteristics, one may know or choose a reasonable difference equation structure for the controller algorithm. Starting with some assumed initial parameter values in the controller equation, the controller can be implemented on the process as shown. The control algorithm is coupled with an on-line recursive estimation algorithm which receives information on the inputs and outputs at each sampling interval and uses this to recursively estimate the optimal controller parameters on-line and to update the controller accordingly. The idea is to use the data collected from the on-line control manipulations to tune the controller directly. 

Kucharski SA, Bartlett RJ (1991) Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations. Theor Chim Acta 80 387 105. 

In what follows, we will develop the conditional mean and covariance for the couple Xk and Yk. This is followed by a description of the Kalman filter and a rapid and practical method for a recursive or iterative calculation of the conditional mean and covariance for the random variable vector... 

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