The alternative to multigrid is to use Newton's method, which requires the solution of large sparse linear equation systems
, usually by preconditioned Krylov subspace methods like GMRES or BiCGSTAB.
In this paper, genetic algorithms were used to solve TSP, 0/1-Knapsack problem Shubert Function, and linear equation system
To further secure the robustness of our findings, we propose an arc-tangent function to replace the surrender rate function in Equation System
4]), were estimated as part of the entire equation system
and are presented, along with complete results, in Tables 5 and 6.
The linearized equation system
describing the dynamics of the model is
Given that 2SLS produces consistent estimates for an equation system
like the one in the present study, it appears that the impact of moving a state's primary or caucus forward in the electoral year works to increase pre-election federal grants to a state.
are added to the overall equation system
, where i indicates the point number in question.
7 discusses the procedure of transforming an equation system
given in levels into linear percentage change form.
Dummy Endogenous Variables in a Simultaneous Equation System
A Dynamic Singular Equation System
of Asset Demand.
The equation system
in 5 is a VAR representation of the structural model because the last term in this expression is serially uncorrelated and each variable is a function of lagged values of all the variables.
The direct solution of the obtained equation system
is quite complex; however, the solution can be found by the method of approximation.
The MAPLE program provides the solutions of the equation system
and reflects them in a graphic form.
x]t-[epsilon]) we obtain the algebraic equation system
(Balcau& Arghir, 2009).
The discrete approximation is especially interesting because it shows the precise sense in which a system of (nonrecursive) simultaneous interdependent equations may be regarded as an approximation to a recursive differential equation system