Übersetzung für "Gradientenverfahren" in Englisch

The filter coefficients are set by iteration according to the gradient procedure with a constant step factor.

An autoencoder is often trained using one of the many variants of backpropagation (such as conjugate gradient method, steepest descent, etc.).

The gradient method enables a local optimum of variables for the operation of the power plant to be found.

Thus, for example, the minimization of a quadratic cost function consisting of cross-correlation terms can be carried out with a gradient process.

The residue is chromatographed on 50 ml of silica gel using toluene and ethyl acetate in a gradient system.

This method uses an appropriate algorithm (e.g. steepest descent) to find the molecular structure of a local energy minimum.

This means velocities are calculated from phase differences in the image data that has been produced using special gradient techniques.

The coefficients can be adjusted automatically to the desired optimal value by various methods, for instance the gradient method.

The feedback control system of that stirring mechanism will operate inversely if the corresponding gradient process uses inverse solution and seed arrangements.

As in all gradient processes, the growing region is separated from the feeding region by a sieve.

Process according to claim 1, wherein the predetermined optimization criteria comprises an adaptation rule operating according to at least one of a method of a least squares error and a method of a gradient process, by which means the parameter vector is continuously adjusted relative to the current measuring process.

The enriched antibiotic Ala(0)-actagardine (280 mg), obtained according to Example 6, is applied to a NucleosilRTM 12C18 AB-HPLC column (width×height=3.2 cm×25 cm) in the gradient procedure using 5% to 30% acetonitrile and 0.05% trifluoroacetic acid.

The enriched antibiotic feglymycin (270 mg), obtained according to Example 6, is separated on a NucleosilRTM 12C18 AB HPLC column (width×height=3.2 cm×25 cm) in a gradient method using 5% to 30% acetonitrile in 0.05% trifluoroacetic acid.

If it is known that a specifically applied approximation function may have only a single minimum in an approximation region, a gradient method by means of a random start vector or one that is established by an approximation in the respective approximation region is advantageous for determining the local minimum in an approximation region.

In such a gradient method, and starting from an initial position, the maximum gradient of the light power is determined in dependence upon a position change of the lamp relative to the illuminating beam path and/or the lamp and the collector optic relative to the illuminating bean path and, thereafter, the lamp and/or the collector optic is shifted in the direction of the maximum gradient of the light power in the illuminating beam path.

The gradient method affords the advantage that it can, on the one hand, be implemented simply and, on the other hand, leads to an optimal adjustment with relatively few iteration steps.

So-called delay correlators are further known which with the aid of a controllable delay path, a control circuit and a voltage-controlled oscillator continuously determine with a mainly analog technique the delay from the zero passage of the differentiated correlation function by a gradient method.

In order to illustrate the influence of a variable step size factor a on the number of iteration intervals i necessary for equalization, FIG. 4 shows the course of the square equalization error I for an automatic and adaptive, decision feedback equalizer E1, where the filter coefficients are determined according to the gradient procedure with a constant step factor and for an equalizer E, where the invention method is employed.

Field of the Invention The present invention relates to an apparatus and method for equalizing an incoming noisy digital signal for an automatic and adaptive decision feedback equalizer where a correction procedure is derived from a reference signal and a filter output signal and where the correction procedure is minimized by iteration according to the gradient procedure and is employed for setting of filter coefficients.

The selection of a constant step factor in the iterative setting of the filter coefficients according to the gradient procedure is a disadvantage in such a circuit.

The gradient coefficients are calculated according to the gradient procedure and are stored at the beginning of the iteration interval for a time, during which the switch is in the one position.

The filter in general comprises a nonrecursive and a recursive part and the filter coeffients of the nonrecursive and of the recursive part are determined by iteration according to the gradient procedure with a constant step factor or by another method.

A preferred embodiment of the structure of an automatic and adaptive decision feedback equalizer is shown in FIG. 2, where the iterative setting of the filter coefficients aj and bk is provided according to the gradient procedure with a variable step size factor a.

For example, numerous iterative optimization techniques such as for example Newton methods, gradient methods, and coordinate exchange methods are described in D. A. Pierre, Optimization Theory with Applications, John Wiley and Sons, New York 1969.

Numerous minimization procedures are described in the prior art; these can essentially be broken down into three categories: Newton methods, gradient methods, and coordinate exchange methods.

In order to find an optimum set of variables for controlling the power plant, it is usual to use gradient methods to find a minimum or maximum for the target function.

Therefore, the comparatively faster gradient methods should in principle be retained, but extended in the form of a hybrid structure by a random-based system to enable the determination of a global optimum of variables.