under the approximation

USAGE SUMMARY

The phrase "under the approximation" is correct and usable in written English.
It can be used when discussing a situation or calculation that is based on a simplified or estimated model rather than exact values. Example: "Under the approximation that the system behaves linearly, we can simplify our calculations significantly."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

11 human-written examples

In addition, under the approximation of uncorrelatedness among the local models, the global filter is shown to be minimum variance.

Applied Soft Computing

Under the approximation, the optimal solution takes the form (43). and the maximal total revenue is (44).

EURASIP Journal on Wireless Communications and Networking

A short period electromagnet undulator has been reported and used for free electron laser experiment under the approximation of infinite permeability of the lamination core.

Optik - International Journal for Light and Electron Optics

The fast computation of (1) can use the standard overlap-add fast convolution [16] under the approximation that filters are constant within each block.

EURASIP Journal on Audio, Speech, and Music Processing

This implies that under the approximation condition those functors are computable, i.e., are completely determined by the regular finite dimensional couple of Banach spaces.

Journal of Functional Analysis

The quantity w A thus represent air particle velocities computed from the Doppler shift under the approximation of mirror-like reflection, when only advection is considered, whereas the quantity w A + C represent air particle velocities computed from the Doppler shift when both advection and compression are considered in the reflection region.

Earth, Planets and Space

Human-verified similar examples from authoritative sources

Similar Expressions

48 human-written examples

Even under such modifications, the approximation of possible attractor points requires the presence of at least one non-differentiated observation in the computational formula.

Journal of Economic Structures

Similar to systems (2.8)–(2.10), under the assumption, the approximation systems (5.1)–(5.2) with possess a unique solution, which continuously depends on initial data.

Advances in Difference Equations

In this case, variational Bayesian under the Laplace approximation iterates between the optimization of parameters and hyperparameters, where the latter basically maximize a regularized quadratic approximation to Equation 13.

Plosone

Under this approximation, the uncertainty in CORIG is given by where we use the property CA and CB are positive.

BMC Psychiatry

Under the Stirling approximation for $n_i \gg 1$ we find which is a discrete version of the Maxwell distribution.

SEP

Expert writing Tips

Best practice

When using the phrase "under the approximation", clearly state what the approximation is and why it is being made. This adds clarity and context to your writing.

Common error

Avoid using "under the approximation" without explicitly defining the approximation being made. This can lead to confusion and misinterpretation.

Linguistic Context

The phrase "under the approximation" serves as an adverbial prepositional phrase, modifying a clause by specifying the conditions or assumptions under which the statement holds true. Ludwig AI confirms its correctness and usability. It is typically used to introduce a caveat or simplification in an argument or calculation.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, the phrase "under the approximation" is a grammatically sound and frequently used expression, particularly in scientific and academic contexts. It serves to introduce a condition or simplification that must be considered when interpreting subsequent statements or calculations. Ludwig AI confirms its validity and usefulness, emphasizing its role in clarifying the scope and limitations of arguments. By explicitly stating the approximation being made, writers can enhance the clarity and rigor of their work. Alternatives such as "assuming the approximation" or "based on the approximation" offer similar meanings, allowing for stylistic variation while maintaining precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

assuming the approximation

Emphasizes the act of making an assumption as a starting point.

based on the approximation

Focuses on the approximation as the foundation for subsequent reasoning.

with the approximation considered

Highlights that the approximation is a factor being taken into account.

considering the approximation

Focuses on taking the approximation into account during analysis.

given the approximation

Indicates that the approximation is a pre-existing condition.

subject to the approximation

Suggests that the approximation introduces a constraint.

relying on the approximation

Emphasizes the dependence on the approximation for the analysis.

making use of the approximation

Highlights the active utilization of the approximation in a process.

utilizing the approximation

Similar to 'making use of' but slightly more formal.

employing the approximation

A more formal synonym for 'using the approximation'.

FAQs

How can I use "under the approximation" in a sentence?

You can use "under the approximation" to introduce a condition or simplification being applied in a calculation or analysis. For example, "Under the approximation that air resistance is negligible, the equation simplifies significantly".

What is a good alternative to "under the approximation"?

Alternatives include "assuming the approximation", "based on the approximation", or "given the approximation", depending on the specific context.

Which is correct, "under the approximation" or "with the approximation"?

Both phrases can be grammatically correct, but they convey slightly different meanings. "Under the approximation" indicates that the subsequent analysis is contingent upon that approximation, while "with the approximation" suggests that the approximation is being taken into account but may not be a strict condition.

What does "under the approximation" mean in scientific writing?

In scientific writing, "under the approximation" indicates that a simplified model or assumption is being used to make calculations or predictions. This is often done to make the problem more tractable or to focus on the most important factors.