The phrase "applies an approximation" is correct and usable in written English.
It can be used in contexts where a method or technique is being employed to estimate or simplify a calculation or concept.
Example: "In this study, the researcher applies an approximation to model the behavior of the system under varying conditions."
Alternatives: "uses an estimate" or "employs a simplification".
Therefore, we firstly apply an approximation approach (AA) to turn the original infinite-dimensional optimization problem into an approximating finite-dimensional one, then design a hybrid algorithm which combines neural network (NN) and particle swarm optimization (PSO) to solve the approximating model.
To avoid this difficulty, we apply an approximation approach (AA) to the proposed two-stage fuzzy MPP model, and turn it into an approximating finite-dimensional optimization one.
At high SNRs, we can apply a approximation, so (d_{mathrm {SR_{1}}}^{m}) can be neglected.
This paper applies a continuous approximation (CA) approach to model the network.
Hence, the composition of the urn is effectively the same throughout the sampling process, and the binomial distribution applies as an approximation.
Design optimization is performed using a multiobjective genetic algorithm while the computational cost due to CFD analysis is reduced significantly by applying an online approximation technique.
Therefore, the rigorous model containing (partial) integro-differential equations is first reduced by applying an integral approximation technique to a model of moments that consists of only a few ordinary differential equations.
These tools ease the interpretation of model behavior by providing diagnostic visualizations of transition matrices, and allow substituting dense transition matrices with a sparse counterpart by applying an iterative approximation algorithm that is independent of model symmetry.
Another rapidly convergent solution of the Marcus–Hush Chidsey integral is available from a later study that elaborates on the results of ref (445) and applies a piecewise polynomial approximation.
Without applying any approximation heuristics, EMD naturally requires a long time to look for the optimal fitness value.
