Iterative play

One can think of a contraction mapping in terms of iterative play player 1 selects some strategy, then player 2 selects a strategy based on the decision by player 1, etc. If the best response mapping is a contraction, the NE obtained as a result of such iterative play is stable but the opposite is not necessarily true, i.e., no matter where the game starts, the final outcome is the same. See also Moulin (1986) for an extensive treatment of stable equilibria. 

Statistical and algebraic methods, too, can be classed as either rugged or not they are rugged when algorithms are chosen that on repetition of the experiment do not get derailed by the random analytical error inherent in every measurement,i° 433 is, when similar coefficients are found for the mathematical model, and equivalent conclusions are drawn. Obviously, the choice of the fitted model plays a pivotal role. If a model is to be fitted by means of an iterative algorithm, the initial guess for the coefficients should not be too critical. In a simple calculation a combination of numbers and truncation errors might lead to a division by zero and crash the computer. If the data evaluation scheme is such that errors of this type could occur, the validation plan must make provisions to test this aspect. 

The discretized equations of the finite volume method are solved through an iterative process. This can sometimes have difficulty converging, especially when the nonlinear terms play a strong role or when turbulence-related quantities such as k and s are changing rapidly, such as near a solid surface. To assist in convergence a relaxation factor can be introduced ... 

We are specifying the type of a system playing a role in a collaboration that is, the view that its collaborators have of it. We already have a initial type model. We may improve it in the light of what we need to say about this action, and iterate between specifying actions and updating the type model. 

Experience has followed an iterative pattern in playing the model exercises against field measurements. Usually, the first indication of the relative importance of variables is seen in bodies of observational data. The next step is to build a model on the basis of either intuition or a deterministic physical equation that reflects the trends seen in the data. The model is then used for the range of conditions in the data base, and uncertainties as to the correctness or completeness of the model become evident. The questions that arise can usually be answered only through further field experimentation. Thus, the models themselves are used in the design of both laboratory and field experiments that will ultimately provide a basis for the improvement of the modeling art. 

These simple model parameters become the main (or "outer loop") iteration variables, the role played by the primitive variables temperature, pressure, vapor and liquid composition and phase rates in Class I and Class II methods. 

The application of constraints should always be prudent and soundly grounded, and constraints should only be set when there is an absolute certainty about the validity of the constraint. Even a potentially useful constraint can play a negative role in the resolution process when factors like experimental noise or instrumental problems distort the related profile or when the profile is modified so roughly that the convergence of the optimization process is seriously damaged. When well implemented and fulfilled by the data set, constraints can be seen as the driving forces of the iterative process to the right solution and, often, they are found not to be active in the last part of the optimization process. 

Combustion reactions are excessively used in propellant systems. The impulse of the gaseous combustion products is used to propel a payload. For obvious technical reasons, the burning temperature of a rocket engine is of interest. The adiabatic flame temperature of combustion (Tad) is the temperature at which reactants and products do not differ in enthalpy. The enthalpies of the components of the system have to be calculated from their standard enthalpy by adding of the enthalpy caused by heating to Tad. This is where the specific heat capacity Cv comes into play. Unfortunately, the component ratios of the system are functions of the temperature, necessitating the use of iterative calculations of Tad. 

Tritium is a very sensitive subject for public acceptance of fusion and will play a central role in the operation of a next-step experimental fusion facility, which will routinely use large amounts of tritium as fuel (e.g., 100 times more in ITER than in present experiments) in a mixture with deuterium. Tritium retention is a regulatory issue since the amount that can potentially be released in an accident sets the limits on plasma operation without removal. Fuel economy has never been an issue in deuterium-fuelled experiments and only recently have the limitations associated with the use of tritium, and its incomplete recovery in experiments in TFTR and in JET, brought the issue of fuel retention under closer scrutiny [56,57]. Table 12.3 provides a list of key quantities related to tritium in existing tokamaks and a next-step device [18,57-59]. 

If the function /is linear in the parameters aj, the fitting procedure is now complete and the values a) are the best values in a least-squares sense. If /is nonhnear in terms of any of the a, values, it is usually necessary to improve the a, values by carrying out another cycle of minimization, in which a] plays the role previously played by a°. The iteration process is repeated as many times as necessary to obtain convergence of the a, values to some predetermined level of accuracy. 

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