degree of approximation with

USAGE SUMMARY

The phrase "degree of approximation with" is correct and usable in written English.
It can be used when discussing the closeness or accuracy of a measurement, estimate, or model in relation to a specific reference or standard. Example: "The degree of approximation with the actual results was satisfactory, indicating that our model is reliable."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

We obtain the rate of approximation of the bivariate operators by using the complete and partial moduli of continuity and the degree of approximation with the aid of a Lipschitz-type space and the Peetre K-functional.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

2. As an application of these methods in theory of Fourier series, we will consider the degree of approximation in accordance with generalized deferred Cesáro means in a generalized Hölder metric in Section 2 and present some applications of the approach concerned with some sequence classes in Section 3.

Journal of Inequalities and Applications

Logically a good degree of approximation is maintained with both the results of the radiological measurement and physiological values [ 50, 52], both in the global movement and in the ones corresponding to every vertebra.

BioMed Research International

In this section, we shall consider the degree of approximation of (fin H alpha,p)) with respect to the norm in the space (H alpha,p)) by the deferred Woronoi-Nörlund means and the deferred Riesz means of the Fourier series of the function f by taking into account the method in [9].

Journal of Inequalities and Applications

Hardy and Littlewood [28] have determined without verification that the class of functions (operatorname{Lip} (alpha, p)) is the same as the class of functions approximable in the (L_{r} -norm with degree of approximation (mathrm{O}(n^{- aL_{r} -normy trigonometric polynomials of order n.

Journal of Inequalities and Applications

This can be done with a degree of approximation that depends only on the accuracy with which the time-varying flow geometry and surface-acoustic boundary conditions can be specified, and replaces Fant's original 'lumped element' heuristic approach.

Journal of Sound and Vibration

This sampling scheme was derived by limit considerations and it works with a degree of approximation for finite samples.

Journal of Statistical Planning and Inference

Although a continuous variable may be assumed to take any real value within a relevant interval, a successful concrete analog computation requires only the measurement of real variables with some degree of approximation.

SEP

The high level of similarity detected allowed us to predict the enzyme classes and, with some degree of approximation, the substrate specificity.

BMC Plant Biology

The degree of approximation of functions whose derivatives coincide a.e. with a function of bounded variation is also discussed.

Journal of Inequalities and Applications

The degree of approximation obtained in this way depends on the modulus of continuity associated with the functions.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When discussing models or calculations, specify what factors influence the "degree of approximation with" real-world data to provide a more complete understanding of the model's limitations and strengths.

Common error

Avoid claiming an unrealistic level of precision when using the phrase "degree of approximation with". Always acknowledge potential sources of error or uncertainty that could affect the final result.

Linguistic Context

The phrase "degree of approximation with" functions as a prepositional phrase that quantifies the level of accuracy or closeness achieved through an approximation method when compared to a specific standard or dataset. According to Ludwig, it is grammatically correct. The phrase is typically employed in technical or scientific contexts.

Expression frequency: Rare

Frequent in

Science

100%

News & Media

0%

Formal & Business

0%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

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Ludwig's WRAP-UP

In summary, "degree of approximation with" is a grammatically correct phrase, as confirmed by Ludwig AI, used to express the accuracy of an approximation relative to a specific standard or dataset. While not frequently encountered, its primary context lies within scientific and technical fields. Alternatives like "level of accuracy with" or "extent of closeness to" may offer similar meanings, but "degree of approximation with" specifically emphasizes the process of approximation itself. When employing this phrase, ensure you clearly define the factors influencing the approximation and avoid overstating its precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

level of accuracy with

Replaces "degree of approximation" with "level of accuracy", emphasizing the precision of the estimation.

extent of closeness to

Focuses on the proximity to a target value rather than the method of estimation.

margin of error in relation to

Highlights the potential error range compared to a known value.

accuracy in comparison with

Emphasizes the comparison of accuracy levels between estimations.

precision with respect to

Stresses the fineness and detail of the estimation in relation to a specific factor.

reliability in connection with

Indicates how trustworthy an approximation is, linking it to another element or condition.

approximation quality concerning

Highlights the level of quality of the approximation, focusing on its merits or faults.

estimation accuracy relative to

Places emphasis on the accuracy of an estimate and its relation to another thing.

closeness of fit with

Highlights the degree to which a model or estimation 'fits' a data set or predicted outcome.

degree of correlation with

Highlights the extent to which two or more variables change together.

FAQs

How can I use "degree of approximation with" in a sentence?

You can use "degree of approximation with" to discuss the accuracy of a model or estimate. For example: "The degree of approximation with the real-world data was high, indicating the model's reliability."

What are some alternatives to "degree of approximation with"?

Some alternatives include "level of accuracy with", "extent of closeness to", or "margin of error in relation to", depending on the context.

Is it better to say "degree of approximation with" or "level of accuracy with"?

Both "degree of approximation with" and "level of accuracy with" are grammatically correct. The best choice depends on the specific nuance you want to convey. "Degree of approximation" emphasizes the process of estimating, while "level of accuracy" focuses on the precision of the result.

In what contexts is "degree of approximation with" commonly used?

"Degree of approximation with" is often used in scientific, mathematical, and engineering contexts when discussing the accuracy of models, simulations, or calculations compared to real-world data or theoretical values.