Computer algorithm

In recent decades, computer scientists have tried to provide computers with the ability to learn. This area of research was summarized under the umbrella term "machine learning . Today machine learning is defined as "the study of computer algorithms that improve automatically through experience [1]. 

In the computer algorithm, division by the diagonal element, multiplication, and subtraction are usually canied out at the same time on each target element in the coefficient matrix, leading to some term like ajk — Next, the same three... 

AI (artificial intelligence) computer algorithms that mimic some aspects of how people think... 

Monte Carlo calculations are somewhat similar to the molecular (or Langevin) dynamics calculations discussed earlier. All function by repeated application of a computational algorithm that generates a new configuration from the current configuration. The... 

The overall objective of research under way as of ca 1997 is to develop a system of sale by description for fine and medium wools whereby the buyer is presented only with measured data on the principal characteristics of the raw wool, as well as an assessment of the less important characteristics by an independent skilled appraiser (8). A scheme for assessing the risk of the presence of colored fiber content in greasy wool has been proposed which depends on production parameters and on the age and sex of the sheep (5). Instmmentation and computer algorithms for the measurement of style and handle... 

As computing capabiUty has improved, the need for automated methods of determining connectivity indexes, as well as group compositions and other stmctural parameters, for existing databases of chemical species has increased in importance. New naming techniques, such as SMILES, have been proposed which can be easily translated to these indexes and parameters by computer algorithms. Discussions of the more recent work in this area are available (281,282). SMILES has been used to input Contaminant stmctures into an expert system for aquatic toxicity prediction by generating LSER parameter values (243,258). 

Inherited errors. These arise as a result of errors occurring in the previous steps of the computational algorithm. 

Because of all these numerical difficulties, neither the LM nor the TG stage-by-stage method is commonly implemented in modern computer algorithms. Nevertheless, the TG method is veiy instructive and is developed in the following example. For a single narrow-boihng feed, the TG manual method is quite efficient. 

Many sophisticated models and correlations have been developed for consequence analysis. Millions of dollars have been spent researching the effects of exposure to toxic materials on the health of animals the effects are extrapolated to predict effects on human health. A considerable empirical database exists on the effects of fires and explosions on structures and equipment. And large, sophisticated experiments are sometimes performed to validate computer algorithms for predicting the atmospheric dispersion of toxic materials. All of these resources can be used to help predict the consequences of accidents. But, you should only perform those consequence analysis steps needed to provide the information required for decision making. 

For 25 years, molecular dynamics simulations of proteins have provided detailed insights into the role of dynamics in biological activity and function [1-3]. The earliest simulations of proteins probed fast vibrational dynamics on a picosecond time scale. Fifteen years later, it proved possible to simulate protein dynamics on a nanosecond time scale. At present it is possible to simulate the dynamics of a solvated protein on the microsecond time scale [4]. These gains have been made through a combination of improved computer processing (Moore s law) and clever computational algorithms [5]. 

A number of workers at Pennsylvania State University examined the push-pull system and found good agreement between their numerical and experimental work. The computational algorithm SIMPLER was used to solve the flow in the two-dimensional push-pull system and it was concluded that for a tank 1.8 m long, the push jet must have an initial velocity of 3.8 m s, that the exhaust flow rate per unit width should be 0.495 m s", and that the ratio of the pull to push flow rates, q /qj, must be between 8.8 and 17.8. 

A computer algorithm SEDNTERP [33,34] has been developed for facilitating the correction in Eq. 3. There is no longer any need (except for imusual solvents) to look up solvent densities and viscosities in the Chemical Rubber Handbook or other data books—a user of the algorithm just has to specify the buffer composition and the temperature of the measurement and the correction is done automatically. 

Maximum entropy A computer algorithm used to predict the theoretical signal from which that observed in a spectrum has been derived. Used in conjunction with electrospray ionization to enhance the quality of the spectra obtained. 

Solution The following is a complete program for performing the calculations. It is written in Basic as an Excel macro. The rather arcane statements needed to display the results on the Excel spreadsheet are shown at the end. They need to be replaced with PRINT statements given a Basic compiler that can write directly to the screen. The programming examples in this text will normally show only the computational algorithm and will leave input and output to the reader. 

Due to serious achievements of the Russian and foreign mathematicians in applied mathematics the majority of mathematical-physics problems may be reduced to computational algorithms, at every step of which 3-point equations like (6) with conditions (8 ) must be solved. 

Let us stress that the computational algorithm given above is stable. 

Stability of difference schemes with respect to coefficients. In solving some or other problems for a differential equation it may happen that coefficients of the equation are specified not exactly, but with some error because they may be determined by means of some computational algorithms or physical measurements, etc. Coefficients of a homogeneous difference scheme are functionals of coefficients of the relevant differential equation. An error in determining coefficients of a scheme may be caused by various... 

The difference boundary-value problem associated with the difference equation (7) of second order can be solved by the standard elimination method, whose computational algorithm is stable, since the conditions Ai 0, Ci > Ai -f Tj+i are certainly true for cr > 0. 

Under such a choice of the computational algorithm the accuracy of scheme (49) will be given special investigation. We are going to show that it converges uniformly with the rate 0 h + r " ) in the case of smooth functions k x) and... 

Some preliminary information on economical schemes. One of the most important issues in numerical methods is the well-founded choice of economical computational algorithms, the realization of which requires a min-... 

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