Nested iterations

Noise allocation followed by scalar quantization and Huffman coding. In this method, no explicit bit allocation is performed. Instead, an amount of allowed noise equal to the estimated masked threshold is calculated for each scalefactor band. The scalefactors are used to perform a coloration of the quantization noise (i.e. they modify the quantization step size for all values within a scalefactor band) and are not the result of a normalization procedure. The quantized values are coded using Huffman coding. The whole process is normally controlled by one or more nested iteration loops. The technique is known as analysis-by-synthesis quantization control. It was first introduced for OCF [Brandenburg, 1987], PXFM [Johnston, 1989b] and ASPEC [Brandenburg et al., 1991], In a practical application, the following computation steps are performed in an iterative fashion ... 

Thus, the approximate Newton search direction in TN methods is obtained by allowing a nonzero residual norm rk = rj = H p + gA at each step. The size of this residual is monitored systematically according to the progress made. This formulation leads to a doubly nested iteration structure for every outer Newton iteration k (associated with xk) there corresponds an inner loop for pk p p 1,. . . . ... 

The changes in SCSSD regard the replacement of the permanent dipole moment of each soft solvent sphere by a couple of dipoles, permanent and induced. The permanent dipoles are kept fixed at the orientations minimizing the energy for the solute ground state, while induced dipoles are allowed to be different for each VB structure. A nested iterative procedure is adopted to fix both dipole distributions, and related contribution to the various elements. 

We believe that a better way to solve the set of Eqs. 11.5.1-11.5.10 is to solve all the equations simultaneously using Newton s method (Algorithm C.2). This approach avoids the nested iterations of the foregoing procedure and keeps both thermodynamic property... 

Figure 7.4. Algorithm for isothermal flash calculation when K-values are composition dependent, (a) Separate nested iterations on iff and (x, y). (h) Simultaneous iteration on and (x. y).

In principle, all the processes described above can be expressed in the form of fully-coupled differential equations and solved mathematically. It is also possible to achieve coupling though hierarchally nested, iterative and convergent mathematical processes. For a simple Darcy diffusion process, the procedure could be ... 

The objects g) appearing here are the nested iterates of the effective coupling function defined previously by Eqs. (5.72)-(5.74). 

Finally, it should be noted that the multigrid method can be used as either an iterative process or as a direct solver (the so-called full multigrid or nested iteration method ). 

FIG. 12 Schematic representation of the iterative scheme. We have two nested iterative loops the time loop (1) for updating the density fields p, and within each time iteration an iterative loop (2) for updating the external potential fields U. We start with an initial guess for the external potential fields. We use Eq. (17) to generate a set of unique density fields. The cohesive chemical potential E [relation (3)] can be calculated from the density fields by Eq. (8). The total chemical potential /x(4) can now be found from Eq. 6. We update the density fields (5) [by using the old and updated fields in Eq. (23)] and accept the density fields if the condition (26) is satisfied. If this is not the case, the external potential fields are updated by a steepest descent method. 

The various procedures that address side chain generation as an energy-driven conformational search can be grouped as systematic, combinatorial, and stochastic methods. The CONGEN procedure " includes five different tree-based implementations of the first two approaches. The first methods, named ALL, generates all possible conformations by a series of nested iterations over every side chain, and hence is limited to 7 or 8 residues. The second method, named FIRST, uses... 

Conditional statements may be nested with other conditional statements and/ or with iterative statements. They are ... 

Iterative statements control how many times a simple statement or a compound statement is repeated, and also may be nested with conditional and/or other iterative statements. They may be... 

For the solution of Equation 10.25 the inverse of matrix A is computed by iterative techniques as opposed to direct methods often employed for matrices of low order. Since matrix A is normally very large, its inverse is more economically found by an iterative method. Many iterative methods have been published such as successive over-relaxation (SOR) and its variants, the strongly implicit procedure (SIP) and its variants, Orthomin and its variants (Stone, 1968), nested factorization (Appleyard and Chesire, 1983) and iterative D4 with minimization (Tan and Let-keman. 1982) to name a few. 

Kim et al. (1990) proposed a nested, nonlinear EVM, following ideas similar to those of Reilly and Patino-Leal (1981). In this approach, the parameter estimation is decoupled from the data reconciliation problem however, the reconciliation problem is optimized at each iteration of the parameter estimation problem. 

Because the workunits require a long calculation (1-2 hours), mechanisms for restarting after an interruption are essential. With the nested loop structure in the calculation, it is easy to write information to a file at the beginning of each of the two outermost iterations (lines 2, 3 in the script. Sect. 7.6). When the calculation starts. 

A nested set of components can be captured in a subprotocol, which facilitates reuse of useful pipeline networks, helps to simplify workflow designs, and can be used to support iterative operations. 

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