The phrase "approximation to replace the" is correct and usable in written English.
It can be used in contexts where you are discussing a method or approach that serves as a substitute or alternative to something else.
Example: "The approximation to replace the original model was necessary due to the complexity of the calculations involved."
Alternatives: "substitute for the" or "alternative to the".
The basic principle of sequential approximations is to replace the given problem by a sequence of quadratic sub-problems that are easier to solve [31, 32].
It explains the use of the multidimensional Hermite polynomial, differing to the Taylor polynomial approximation, to approximate the objective function to replace the finite element computation in optimization.
(2335) In addition to the modeling framework, individual models differ in the quality of the approximations, which are used to replace the model parameters, which would be too tedious to measure for each chemical.
An attempt is also made to replace the approximation from UWT with Intrinsic Mode Function (IMF) derived from the Empirical Mode Decomposition (EMD).
The dual constraint relaxation reflects in two parts: on one hand, the objective function based on local region is exploited to replace the pointwise approximation method; on the other hand, considering the variance of local intensity distribution and the reliability of polynomial approximation, we utilize a Gaussian pyramid convolution strategy to devise polynomial fitting.
For example, it is straightforward to extend the underlying model to include, e.g., inhomogeneous material properties or to replace the diffusion approximation by a more complicated model such as the radiative transfer equation.
The idea for overcoming this drawback, proposed in[16], is to replace the part of the approximation (11) that computes the average value of input arguments x i by the part that will compute the sum of all x i and then divide it by a certain parameter N, suitably selected so as to optimize the performance of the algorithm.
Kriging approximation has been widely used in reliability-based design optimization (RBDO) to replace the complex black-box performance functions.
Approximation models are established based on the Ellipsoidal Basis Function (EBF) neural network to replace the finite element analysis in layout optimizers.
When identifying a continuous-time AR process from discrete-time data, an obvious approach is to replace the derivative operator in the continuous-time model by an approximation.
