approximation with

USAGE SUMMARY

The phrase "approximation with" is correct and usable in written English.
It can be used when discussing a method or process that involves estimating or coming close to a certain value or result. Example: "The approximation with the new formula yielded results that were surprisingly accurate."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The approximation with two terms is equal to the approximate length of cubic parabola.

European Transport Research Review

A Hardware-Independent Fast Logarithm Approximation with Adjustable Accuracy.

University of California, Berkeley

Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior.

Nature

Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic-Behavior.

Nature

The first result pertains to uniform approximation with Bernstein polynomials.

European Journal of Combinatorics

ApproximationDemo.m is a demonstration program that does function approximation with interpolation, Hermite interpolation, and clamped splines.

University of California, Berkeley

– Non-strongly-convex smooth stochastic approximation with convergence rate by Francis Bach and Eric Moulines.

Princeton University

LPA molecular species were selected with the closest possible approximation with available LPA standards for concentration calculation.

Nature

Contours were smoothed via a polynomial approximation with exponential kernel (PAEK) algorithm using a tolerance value of 60 m.

University of California, Berkeley

First principle calculations were performed using the generalized gradient approximation with PBEsol exchange correlation functional47, as implemented in the pwscf code, within Quantum Espresso (QE) package48.

Nature

The energy of the residual error of this approximation with NNMF was 13.3% of the energy of the data matrix (see Methods section).

Nature

Expert writing Tips

Best practice

When using "approximation with", ensure that the method or tool being used for the approximation is clearly specified to avoid ambiguity. For example, "approximation with a linear model" is clearer than simply "approximation with".

Common error

Avoid using "approximation with" without specifying the context or method. Saying "the result was obtained through approximation with..." leaves the reader wondering about the specific technique used and can weaken your argument.

Linguistic Context

The phrase "approximation with" functions as a prepositional phrase that specifies the means or method used to achieve an approximate result. Ludwig examples show its use in describing calculations, models, or techniques employed for estimation.

Expression frequency: Very common

Frequent in

Science

78%

Academia

18%

News & Media

4%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "approximation with" is a grammatically correct and commonly used prepositional phrase, particularly in scientific and academic writing. According to Ludwig AI, it serves to specify the means or method used to achieve an approximate result. The primary contexts are science and academia, with occasional appearances in news and media. When using "approximation with", ensure clarity by specifying the method or tool being utilized. Consider alternatives like "estimation using" or "calculation involving" for nuanced variations.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

approximate solution utilizing

Focuses on the solution derived from approximation, emphasizing the tools used.

close estimate using

Emphasizes the similarity/closeness of the result when estimating.

estimation using

Focuses on the method of estimation rather than the result of approximating.

calculation involving

Emphasizes the computational aspect of the approximation process.

estimation in

Highlights the domain or context where estimation occurs.

assessment through

Suggests a formal evaluation leading to an approximation.

evaluation employing

Highlights a structured evaluation process used to create the approximation.

numerical method for

Specifies that approximation is achieved through computational techniques.

modeling via

Indicates that a model is used to create an approximation.

rough estimate by means of

Highlights the approximate and indirect nature of the estimation.

FAQs

How do I use "approximation with" in a sentence?

Use "approximation with" to indicate the method or tool used to estimate a value or result. For example, "The model's accuracy was improved through approximation with advanced algorithms."

What are some alternatives to "approximation with"?

You can use alternatives like "estimation using", "calculation involving", or "modeling via" depending on the context.

Is there a difference between "approximation with" and "estimation using"?

"Approximation with" generally implies a process of coming close to a value, while "estimation using" emphasizes the act of making an informed guess or judgment with a particular method.

When is it appropriate to use "approximation with" in formal writing?

It's appropriate in scientific, academic, or technical contexts when describing a method that provides an estimate or inexact solution, particularly when the method itself is relevant to the discussion.