The phrase "approximated to within" is correct and usable in written English.
It can be used when discussing measurements, estimates, or calculations that are close to a certain value or range.
Example: "The final result was approximated to within 5% of the actual value."
Alternatives: "estimated to within" or "calculated to within".
As shown by Mittal and Schulz [20], the optimum value of problem (P) cannot be approximated to within any factor unless (mathit{NP}=P).
As shown by Mittal and Schulz [9], the optimum value of problem (P) cannot be approximated to within any factor unless (mathrm{P}=mathrm{NP}).
Our main result is that even a very special case of this problem cannot be approximated to within a factor 2log1−ε|D| if D is the set of demands.
We prove that the Minimum Links problem cannot be approximated to within a ratio of O(2log1−ϵn), for any fixed ϵ>0, unless NP⊆DTIME npolylog(n)), where n is the number of nodes in the network.
The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition.
For larger systems, G3(MP2 -RAD barriers can be approximated (to within 1 kJ mol−1) via an ONIOM-based approach in which the core is studied at G3(MP2 -RAD and the substituent effects are MP2 -RADwith ROMP2/6-311+G(3df,2p).
AECs are closely approximated to the mesenchymal (fibroblast) cells within the lung, and are believed to play an important role in homeostasis between epithelial and mesenchymal cells.
Neighbourhoods are typically defined as the area within 800 m (approximating to a 10 min walk) of a home location.
Trevisan [ 14] showed that the hitting set problem, when the size of the input sets is bounded by B ≥ 2 (B = 6 in our case), is hard to approximate to within B - 1 19.
Log-linear models introduce bias terms that can be approximated using within-group variances (appendix 2).
We ran the model at all FIA plot locations (approximated within 500 m to preclude potential disclosure of confidential locations) within the ecoregion to the stand age in the plot data, and compared predicted and observed net stem production using a range of possible parameter values.
