the same approximation

USAGE SUMMARY

The phrase "the same approximation" is correct and usable in written English.
It can be used when referring to a previously mentioned estimation or calculation that remains unchanged or consistent. Example: "In our calculations, we found that using the same approximation yielded similar results across different scenarios."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

50 human-written examples

We present a simple combinatorial linear time algorithm with the same approximation guarantee.

Operations Research Letters

Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach.

University of California, Berkeley

For non-amenable groups the same approximation property is a necessary condition for being matricially stable.

Journal of Functional Analysis

The same approximation used for processing the experimental datasets applies to simulation data, then the same assumptions are considered.

Chemical Engineering Science

The same approximation applies to hearing voices (or is that the brain, not the ears?) being at a hearing, to hear from someone (by letter or email), or indeed the phrase "Hear!

The Guardian - Music

Theoretical analysis and the experimental results showed that the new algorithm requires considerably less geometric data at the same approximation error than the traditional one.

Advances in Engineering Software

Human-verified similar examples from authoritative sources

Similar Expressions

10 human-written examples

Therefore, the same approximations of MMIB functions for 4 QAM, 16 QAM, and 64 QAM modulations can be utilized in the case of the FBMC transmission.

EURASIP Journal on Advances in Signal Processing

In the same manner, we can obtain further approximations (v_{3} x,t), ldots) Setting (beta=1) in the first approximation (24) and the second approximation (25) and after some simplifications, we obtain the same approximations as (15) and (16) on returning to the original variable.

Advances in Difference Equations

Then, following the same approximations that led to Equation (8), (14) where C i is the proportionality constant such that ∑ j ′=1 m π ij ′=1.

Bioinformatics

Although the Satterthwaite and K-R methods have the same approximations of DDF in this analysis, the K-R method has the smaller F value and more conservative p value due to its further inflation of the standard error estimation (0.4507 vs 0.4485).

BMC Medical Research Methodology

The probability density that haplotype i is seeded at time t is given by the rate α(t) of establishing new haplotypes multiplied by the probability of having i − 1 haplotypes at time t, (3) p i (t ) = α (t ) e − λ (t ) λ (t ) i − 1 (i − 1 ) ! ∝ e − (u / s ) e s t + i s t, where we have used the same approximations as in Equation 2 and dropped factors independent of t that ensure normalization.

Genetics

Expert writing Tips

Best practice

When using "the same approximation", ensure that the context clearly establishes what the original approximation is, to avoid ambiguity. Be specific about the conditions under which the approximation remains valid.

Common error

A common mistake is assuming "the same approximation" is valid across all scenarios. Always verify the approximation's suitability for the new context, as its accuracy can vary significantly with different parameters or conditions.

Linguistic Context

The phrase "the same approximation" functions as a noun phrase, often used as an object or complement in a sentence. It refers to a previously mentioned estimation or calculation method that is being consistently applied. According to Ludwig AI, it is grammatically correct.

Expression frequency: Very common

Frequent in

Science

81%

Academia

10%

News & Media

5%

Less common in

Formal & Business

1%

Wiki

1%

Reference

1%

Ludwig's WRAP-UP

In summary, the phrase "the same approximation" is a grammatically correct and frequently used noun phrase, particularly in scientific and academic contexts. Ludwig AI confirms its validity. Its primary function is to maintain consistency and comparability in analyses by ensuring a uniform estimation method. While versatile, it's crucial to ensure that the approximation's applicability remains valid across different scenarios, avoiding overgeneralization. Alternative expressions include "an equivalent estimate" and "a similar estimation", which can be used to add variety while retaining the core meaning. Always specify the original approximation to prevent ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

an equivalent estimate

Replaces "approximation" with "estimate", implying a calculated value, while "equivalent" maintains the sense of sameness.

a similar estimation

Uses "estimation" instead of "approximation" with "similar" to convey nearly the same result.

an identical assessment

Substitutes "assessment" for "approximation", highlighting the evaluation aspect, while "identical" emphasizes exact correspondence.

a comparable calculation

Replaces "approximation" with "calculation", focusing on the computational aspect, with "comparable" indicating near equivalence.

a consistent evaluation

Uses "evaluation" in place of "approximation", emphasizing judgment aspect while "consistent" shows the uniformity.

the matching estimate

Replaces "same" with "matching", which is a variation to the original expression, and replaces "approximation" with "estimate".

an analogous estimation

Uses "analogous" instead of "same", which is a variation to the original expression, and replaces "approximation" with "estimation".

a corresponding assessment

Replaces "approximation" with "assessment", which is a variation to the original expression, and uses "corresponding" instead of "same".

the equivalent calculation

Uses "equivalent" instead of "same", which is a variation to the original expression, and replaces "approximation" with "calculation".

a uniform valuation

Replaces both "same" and "approximation" with completely different synonyms, namely "uniform" and "valuation" respectively.

FAQs

When is it appropriate to use "the same approximation" in a sentence?

Use "the same approximation" when you are referring back to a previously defined or understood method of estimation. It implies consistency in the approach used.

What are some alternatives to saying "the same approximation"?

You could use phrases like "an equivalent estimate", "a similar estimation", or "an identical assessment" depending on the nuance you wish to convey.

Is it better to say "similar approximation" or "the same approximation"?

"The same approximation" indicates that the exact same method is being used. "Similar approximation" implies that the method is not exactly the same, but close enough for comparative purposes.

How does using "the same approximation" impact the results of a study?

Using "the same approximation" ensures consistency in the calculations, which can help to make results comparable across different samples or conditions, assuming the approximation remains valid in each context.