Linear algorithm

The least-squares algorithm used is basically the linearized non-linear algorithm which is of common use in crystallographic structure... 

Sanders, Alton F., "Graph Theoretical Constraints on Linearization Algorithms for Canonical Chemical Nomenclature," presented at the 169th National Meeting of the American Chemical Society, Philadelphia, April, 1975. 

The sensitivity trajectory W t), when requested, is computed by the method of Caracotsios and Stewart (1985), extended here to include Eq. (B.l-4b). The sensitivities are computed at to and after each step, via a direct linear algorithm that utilizes the current matrix G of equation (B.l-5b) or (B.l-5a) to solve equation (B.l-4b) or a backward-difference form of (B.l-4a). 

Some of the more current RNGs use alternative algorithms, like nonlinear recursion or multiple recursion, but these are beyond the scope of this chapter. These new algorithms have periods of more than 2 ° (the Mercenne Twister has a period of 2 - 1 ) and therefore have better randomness properties. They are five- to tenfold slower than linear algorithms, however. 

Aringhieri, R., Hansen, P. and Malucelli, F. (2001) A linear algorithm for the hyper-Wiener index of... 

Vukicevic, D. and Graovac, A. (2004c) Valence connectivity versus Randic, Zagreb and modified Zagreb index a linear algorithm to check discriminative properties of indices in acyclic molecular graphs. Croat. Chem. Acta, 77, 501-508. 

Today s multivariable controllers are mainly linear algorithms. Depending on the process, there can be significant advantages to optimizing the process using a nonlinear model. Most nonlinear models today are steady-state, rigorous, heat and mass balance models and are built separate from the multivariable controller. 

One of the most popular applications of expert systems is an intelligent job aid (Harmon, 1987 Tieman Markle, 1984). A job aid is any structured information device that an individual consults to help perform some task. Job aids are often used in place of instruction when the task performance is simple enough and non-recurrent. Job aids use linear, algorithmic logic to ensure that the performer is able to complete the task correctly. Expert systems can perform as job aids more effectively than traditional, print, linear job aids because they can represent more complex problems and because they do not use a linear procedure to solve the problem, like most job aids. The reasoning pattern of an expert system is more flexible. Welsh and Wilson (1987) have identified characteristics of expert systems as intelligent job aids ... 

As the elements in the Jacobian Jo depend on the location b in the parameter space and therefore reflect local properties, a single application of the linear algorithm does not yield the optimal parameter estimates. These are determined by successive approximations ... 

Hansen P, Zheng ML (1992b) A Linear Algorithm for Fixed Bonds in Hexagonal Systems. J Mol Struct (Theochem) 257 75... 

Tuning is calculated using the same approach as for the linear algorithm. We first determine for a proportional-only controller based on restoring the flow balance when... 

Following the same approach as the linear algorithm, the full tuning becomes... 

J. Bhasker and S. Sahni. A Linear Algorithm to Find a Rectangular Dual of a Planar Triangulated Graph. In Proc. of 23th Design Automation Conference, June 1986. 

Kernel Functions Technique for Nonlinear Data Processing by Linear Algorithm... 

Besides the straightforward fingerprints studies, XANES can also be applied to quantitative speciation. This is because XAS is a local probe teehnique, which implies no long-range order in the sample is required. Therefore, if the absorbing atoms are present in the sample at two different sites, the XANES spectrum obtained from this material can be represented by the weighted addition of the spectra of suitable reference samples. For many systems, XANES analysis based on linear combinations of known spectra from model compounds is sufficient to estimate ratios of different species. More sophisticated linear algorithms, such as principle component analysis and factor analysis, can also be applied to XANES spectra. ... 

Site Response for Seismic Hazard Assessment, Fig. 10 Equivalent linear algorithm (Modified from Lanzo and... 

Equation 6.1 is essentially an empirical model, likely selected for its convenience in fitting experimental data, using a linear algorithm for instance the least square method. It is worth noting that considering the variation of... 

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