The phrase "approximated with the" is correct and usable in written English.
It can be used when discussing how something is estimated or represented in relation to another thing.
Example: "The value of pi can be approximated with the fraction 22/7 for practical calculations."
Alternatives: "estimated using the" or "represented by the".
Table 1 also shows that, in general, the point estimates of the Bayesian estimates (BLOR and BLOR*) are similar to the MLEs (MLLOR, and MLLOR*, which was approximated with the MLE with probit ordinal regression); however, the approximations (BLOR* and MLLOR*) have greater bias and SD.
The time derivatives are approximated with the Crank-Nicolson method [ 32] that yields an implicit approximation to the solution of the initial value problem y′ = f x, y) with y x0) = y0 at x for a given time step h.
Inhomogeneities in modified Helmholtz equations are approximated with the thin plated radial basis functions.
In the present study, shoulder broadness (SB), H0, is approximated with the intercept of the linear portion at the Log I = 0.
The coefficients of potential and capacitance of a pair of conductor are approximated with the first terms of an expansion formula in the inverse of their distance.
The number of inaccurate sediment estimations decreased significantly and the cumulative sediment sum is closely approximated with the wavelet ANN method.
The coupling between global and local modes is approximated with the coupling between a travelling global wave and uncorrelated local waves.
The classical Robertson test problem for chemical reactions which is known for its stiffness is excellently approximated with the modified Patankar-type scheme.
The output of a system due to a change of its parameters is often approximated with the sensitivity matrix from the first order Taylor series.
Similar to the mean-value first order Second Moment (MVFOSM) approach, a performance function is approximated with the first order Taylor expansion at the mean values of random input variables.
The first modelling method is based on a theory of mass transfer with simultaneous catalytic reaction; in the second method the reaction kinetics and mass transfer phenomena are approximated with the neural network.
