Variance minimization technique

In the optimization of the wave function, we use the modification of the variance minimization technique [35]. In the original scheme, the sample points are generated according to the initial wave function and are fixed during optimization. In our study, we select the sample points used in the optimization as follows First, we generate... 

Probabilistic techniques of estimation provide some Insights Into the potential error of estimation. In the case of krlglng, the variable pCic) spread over the site A is first elevated to the status of a random function PC c). An estimator P (2c) is then built to minimize the estimation variance E [P(2c)-P (2c) ], defined as the expected squared error ( ). The krlglng process not only provides the estimated values pCiyc) from which a kriged map can be produced, but also the corresponding minimum estimation variances 0 (39 ) ... 

The proposed technique is based on an extension to time-varying systems of Wiener s optimal filtering method (l-3). The estimation of the corrected chromato gram is optimal in the sense of minimizing the estimation error variance. A test for verifying the results is proposed, which is based on a comparison between the "innovations" sequence and its corresponding expected standard deviation. The technique is tested on both synthetic and experimental examples, and compared with an available recursive algorithm based on the Kalman filter ( ). 

The sophistication of fiber diffraction has grown along with the development of digital computers. These techniques started with the calculation of diffraction intensities for a few proposed models for comparison with the diffraction pattern. At present, parameters of the models can be varied to produce the minimal variance for the observed and calculated diffraction intensities and simultaneously the minimal stereochemical or packing energy. 

A one-dimensional search optimization technique, such as the Fibonacci search, is employed to minimize Equation 8-113. A computer program (PROG81) was developed to estimate the equivalent number of ideal tanks N for the given effluent tracer response versus time data. Additionally, the program calculates the mean residence time, variance, dimensionless variance, dispersion number, and the Peclet number. 

If the function may be made linear with respect to its unknown parameters by a suitable transformation, then it may be fitted by the Linearized Least Squares method (10) so as to minimize the root mean square error in the original (untransformed) space. The essence of this technique is to use weighted (linear) least squares to effect a non-linear least squares fit. Assume that the equation has been transformed into an equal variance space and let... 

For a given value of O and y in the log-normal distribution function, the mean and variance of the distribution function were computed and compared with the mean and variance of the measured bubble lengths. A regula falsi technique was used to minimize the difference between observed and calculated mean and variance. The values of O and y that minimized the difference between observed and calculated mean and variance were then employed in Equation (1) to describe the local bubble diameter distribution. The Sauter mean bubble diameter was evaluated from the second and third moments of Equation (4). 

In the present application of two combined techniques, the Kalman filt and the minimization procedure, an appropriate aror function should be con dered such that the values of Tj at convergence correspond as much as possible to the model with the minimum error and to the concentration estimates with the minimum variances. The onployed error function is the sum of two terms ... 

But instead of solving the n-coupled non-linear equations given in (12) by minimizing as it merely represents satisfaction of the variance stationarity condition as opposed to the absolute minimization of V, direct minimization of V by the SAM appears to be a perfectly feasible proposition [28]. Having thus made the advocated methodologies transparent, we now turn to some simple minded applications of the techniques to the... 

The calibration model referred to a partial least squares regression (PLSR) is a relatively modem technique, developed and popularized in analytical science by Wold. The method differs from PCR by including the dependent variable in the data compression and decomposition operations, i.e. both y and x data are actively used in the data analysis. This action serves to minimize the potential effects of jc variables having large variances but which are irrelevant to the calibration model. The simultaneous use of X and y information makes the method more complex than PCR as two loading vectors are required to provide orthogonality of the factors. 

M = K0(tdil)-ico/[4ziRl(7lie2I0(KRl)],al=a0N I R2b, a, =a0N R2-R2 x)IR2b, l,m = l,2,3...Nc. The minimal root of this equation gives the wave number of the surface wave. For comparing, we also developed many-body technique for calculation of the dispersion properties of CNT bundle with N <73. The results obtained by different methods are in a good agreement with the variance less... 

The smooth operation flow of materials and products are further enhanced by Lean Sigma methodology where the variances within processes and between workstations are minimized by the statistical techniques of Statistical Process Control (see Basu, 2004, pp. 151-157). 

A variety of functional forms has been used for several very small systems. These include the molecule H2, the ion H3, and the dimer He-He for which Hylleraas functions. Singer polymals, and explicitly correlated Gaussian functions of very high accuracies have been used in QMC of all types. The optimization of these functions has usually been carried out by means of the technique of minimizing the variance in local energies described by Conroy the 1960s. In fact, it has only rarely been done in any other way. 

Scanning techniques can be employed for the measurement of the analyte ion currents at the appropriate m/z values. When scanning is used, several replicate scans for each sample analysis should be employed to minimize the measurement variance of each standard and sample. If scanning is used for quantitation, either peak heights or peak areas can be used to establish the intensity of the ion current. 

---