The phrase "approximations to make" is correct and usable in written English.
It can be used when discussing the need to create or consider estimates or rough calculations in a particular context.
Example: "In our analysis, we have several approximations to make before reaching a final conclusion."
Alternatives: "estimates to consider" or "calculations to perform".
This requires some approximations to make the SVD tractable, like hierarchically extracting singular vectors until their associated singular values become irrelevant (see, e.g., [2, 9]).
However, this rule is not true in a strict sense for arbitrary driving processes and requires some mild approximations to make it a more general statement.
In this paper the rate expression is simplified by a number of approximations to make it suitable for practical applications without loosing significant accuracy.
For this purpose, we return to Equation (1) and assume that a range of wavelengths can be found for which the following approximations hold: sinc π πa cos ψ ≈ 1, sinc π πa sin ψ ≈ 1, and exp − 2 π sa z b ≈ 0. For these approximations to make sense, the bodies must in general be large in depth compared to their horizontal dimensions.
Therefore, we present an algorithm that makes two approximations to make the solution tractable.
Furthermore, due to the interference uncertainty, we formed the interference constraint as the chance constraint and implied Bernstein's approximation to make it tractable.
Using this Markov process, we have calculated the exact solution and proposed an approximation to make the problem much easier to solve, without changing its characteristics.
We need one additional approximation to make further progress.
While clearly, no two hurricane wind fields are the same, the simulation of a known storm provides some basis for comparison, given the approximations needed to make a hindcast, which are amplified when making a forecast.
Furthermore, the constrained low-rank approximation has been proposed to perform low-rank approximation automatically to make the kernel projection feasible for classification.
We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation.
