The phrase "approximation is needed" is correct and usable in written English.
It can be used in contexts where a rough estimate or a close calculation is required rather than an exact figure.
Example: "In this case, approximation is needed to simplify the calculations and make the problem more manageable."
Alternatives: "an estimate is required" or "a rough calculation is necessary."
To calculate (19) with the use of (9) (and with isotropic initial fiber orientation tensor (bar {boldsymbol {N}}(0))), a closure approximation is needed to approximate (bar {mathbb {N}}) based on (bar {boldsymbol {N}}) in each time step, since otherwise the expression (9) is undetermined.
Problems with data that comes with built-in noise from the real world, or where some approximation is needed, are the best fits.
Thus, some approximation is needed in practice.
Therefore, some form of approximation is needed.
Pulse shapes with even better frequency localization may be used if higher approximation is needed.
For the general case, an approximation is needed (but other arguments can also apply, see, for instance, [84], Section 5.1). square ). square
Cutpoint shift can be calculated accurately for rectangular nozzle but for round nozzle additional approximations are needed.
Since the yield condition for frame structures is non-linear, piecewise linear approximations are needed in order to apply linear optimization methods.
In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient.
Compared with the existing works, the prominent advantage is that no parameter identifications and no neural or fuzzy nonlinear approximations are needed, which decreases the complexity of robust controller design dramatically.
The first term of Eq. (2) may be expanded in an infinite series, and therefore approximations are needed to successfully model the expression.
