by approximating

USAGE SUMMARY

The phrase "by approximating" is a correct and commonly used construction in written English.
It can be used to describe a method or approach of estimating or calculating something. Example: "By approximating the cost of materials, we were able to create a more accurate budget for the project." Here, "by approximating" indicates that the cost was not precisely calculated, but rather estimated or rounded off in order to come up with a practical budget.

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

PNN is an approximation of the Bayesian classifier by approximating these distributions using the Parzen window approach.

Nonlinear Analysis: Theory, Methods & Applications

By approximating also by, (5) shows the following ratio is approximately constant: (17).

EURASIP Journal on Information Security

They wanted to celebrate their union by approximating the highly publicized round-the-world flight he had made in 1934.

The New York Times

So I went out into the places where the story had happened, and tried to feel my way into his world by approximating an experience of it.

The Guardian - Books

By approximating these changes as zero, my work has thereby understated the amount by which marginal labor income tax rates have increased since 2007.

The New York Times

By approximating the yield for each scenario, the optimal configuration can then be chosen.

Solar Energy

NDP can sensibly mitigate this drawback by approximating the solution with ANNs.

IFAC Proceedings Volumes

Approximate computing at algorithm level reduces the computational complexity by approximating or skipping computational blocks.

Journal of Systems Architecture

The dam block heat flux is estimated by approximating it as a semi-infinite body.

Applied Thermal Engineering

Rotation was achieved by approximating short parallel incisions on the dorsum of both corpora cavernosa.

European Urology

The Taylor series numerical method is addressed by approximating the solution to the SDRE.

Acta Astronautica

Expert writing Tips

Best practice

When using "by approximating", ensure the approximation method is clear and justified within your context. This enhances the credibility of your analysis.

Common error

Avoid presenting results obtained "by approximating" as precise values. Always acknowledge the inherent limitations of the approximation method to maintain transparency and avoid misleading your audience.

Linguistic Context

The phrase "by approximating" functions as an adverbial phrase modifying a verb. It describes the method or process used to achieve a certain result. Ludwig's examples illustrate its use in scientific and technical contexts to explain how solutions or models were simplified.

Expression frequency: Very common

Frequent in

Science

85%

News & Media

10%

Formal & Business

5%

Less common in

Wiki

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

The phrase "by approximating" is a versatile tool for explaining methodologies involving simplification or estimation. Ludwig AI indicates its grammatical correctness and frequent use, especially in scientific and technical writing. Remember to justify your approximations and avoid overstating the accuracy of the results. When writing, consider alternatives such as "by estimating" or "using an approximation" for nuanced expression. By understanding its function and usage, you can effectively communicate complex ideas with clarity and precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

by estimating

A more direct verb form of approximating.

using an approximation

Highlights the tool used for approximation.

through estimation

Focuses on the act of estimating, rather than the method.

via estimation

Similar to "through estimation", emphasizing the means by which something is determined.

through simplification

Highlights the act of simplifying complex data.

on the basis of approximation

Formal phrasing, putting emphasis on the foundation for the estimate.

by way of approximation

Slightly more formal, emphasizing the pathway to estimation.

with a rough calculation

Emphasizes the lack of precision in the calculation.

via modeling

Emphasizes using a model to represent the approximated concept.

in the approximate

Focuses on working within the confines of an approximate value.

FAQs

How can I use "by approximating" in a sentence?

Use "by approximating" to indicate that a result or value has been estimated or simplified, rather than precisely calculated. For example, "We simplified the model "by approximating" the fluid as incompressible".

What are some alternatives to "by approximating"?

You can use alternatives like "by estimating", "through estimation", or "using an approximation" depending on the specific nuance you want to convey.

When is it appropriate to use approximations in calculations?

Approximations are appropriate when exact calculations are too complex, unnecessary for the desired outcome, or when precise data is unavailable. It's crucial to acknowledge the level of error introduced "by approximating".

What's the difference between "by estimating" and "by approximating"?

"By estimating" generally refers to making a rough calculation or judgment, while ""by approximating"" often implies using a specific method to simplify a complex problem or value. The difference is subtle and context-dependent.