by approximation with

USAGE SUMMARY

The phrase "by approximation with" is correct and can be used in written English.
You can use it to introduce an idea or concept that you intend to compare or contrast with another idea or concept. For example: By approximation with earlier models, this newer version is much more powerful.

✓ Grammatically correct

Science

Wiki

News & Media

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

Its curvature is obtained first by identifying a set of control points and, afterwards, by building up a smoothed skeleton by approximation with a curve, which is finally moved during the animation phase.

EURASIP Journal on Image and Video Processing

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

Orange broken line is approximate straight line with gradient p, which was computed by linear approximation with the least squares method.

Earth, Planets and Space

AMMR was standardized by age (SRA) through direct method, and the standard error was calculated by Poisson approximation with a 95% reliability interval.

BMC Cancer

As shown in Fig. 4, we computed the gradient p by linear approximation with the least squares method.

Earth, Planets and Space

Theses relations related to the positive void reactivity have been formularized by the approximation with few parameters within several percent respectively as well as the TRU CR, indicating that one of dominating parameters is the ratio of sodium loss to plutonium fissile in the void reactivity at large fast reactors.

Annals of Nuclear Energy

The sample size for the planned large cohort study was calculated by normal approximation with continuity correction and the power was 90%.

BMJ Open

The temperature trend was obtained by approximation of the series with distance-weighted least square smoothing technique (DWLS) and tension parameter set at 0. In order to avoid inclusion of the temperature when the probe was out, the trend was calculated only from the values of temperature exceeding the core trunk temperature.

Acta Neurochirurgica

Select the centre point (B) on the base of thumb by approximation or by measurements with a scale as shown in the diagram.

WikiHow

Moreover, to comprehensively investigate the differences between deterministic and reliability based design optimization, single objective and multiple objective RBDO are established by integrating Kriging approximation with Monte Carlo Simulation (MCS).

Thin-Walled Structures

We used generalized linear mixed models (GLMM) fitted by the Laplace approximation with an assumed quasipoisson distribution and a log-link [38] to test for the effects of vertebrate exclusion on leaf damage (mean damage of leaf area and mean number of holes per leaf) by taking repeated samplings into account.

Plosone

Combining this with Theorem 7.3 by approximation we thus obtain the following multidimensional version of the Suita conjecture: For a pseudoconvex (Omega ) and (win Omega ) one has begin{aligned} K_Omega (w,w ge frac{1}{lambda (I^A_Omega (w))}.

Bulletin of Mathematical Sciences

Expert writing Tips

Best practice

When using "by approximation with", clearly define what is being approximated and what it's being approximated with to avoid ambiguity.

Common error

Avoid using "by approximation with" when a precise calculation is available. This phrase suggests an estimate when accuracy is achievable.

Linguistic Context

The phrase "by approximation with" functions as a prepositional modifier, indicating the method or manner in which something is being performed or understood. It suggests an inexactness or estimation in relation to another element. Ludwig AI confirms that is grammatically correct.

Expression frequency: Rare

Frequent in

Science

75%

Wiki

12%

News & Media

12%

Less common in

Formal & Business

0%

Academia

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "by approximation with" is a grammatically sound prepositional phrase primarily used in scientific and technical writing to indicate a method involving estimation or comparison. As Ludwig AI confirms, the phrase is correct. While not particularly common, its usage implies a deliberate choice to convey a degree of inexactness rather than precise calculation. It's crucial to provide context when employing this phrase, ensuring clarity about what is being approximated and what it's being approximated with. Alternatives such as "by estimation with" or "using approximation with" may offer nuanced options depending on the specific meaning you wish to convey. Though the phrase appears most often in scientific contexts, it can be appropriate in other formal settings when the intent is to describe an estimation method.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

by estimation with

Focuses on the estimation aspect, highlighting the process of approximating a value or result.

by rough calculation with

Emphasizes the imprecise nature of the calculation being performed alongside something else.

through estimation with

Similar to using approximation but uses "estimation" to convey a less precise calculation.

by means of approximation with

Adds formality, highlighting the method or tool used for approximation.

via approximation along with

Specifies that something is done by means of approximation and also mentions an accompanying element.

using approximation with

Highlights the use of approximation as a tool alongside something.

in approximate relation to

Expresses the result or a state obtained after an approximation has been made instead of the action.

in the vicinity of

Signifies a location or condition reached after an approximated measure.

in close estimation to

Expresses proximity through calculation and not physical location.

approximating in conjunction with

This alternative explicitly mentions a secondary action accompanying the first action of approximation.

FAQs

How can I use "by approximation with" in a sentence?

You can use "by approximation with" to indicate a method or comparison where one element is estimated in relation to another. For example, "The curve was smoothed "by approximation with" a curve".

What does "by approximation with" mean?

"By approximation with" means using an estimated or inexact method alongside or in comparison to something else. It suggests that precision is not the primary focus.

What are some alternatives to "by approximation with"?

Alternatives include "by estimation with", "using approximation with", or "in approximate relation to", depending on the specific nuance you want to convey.

Is it correct to say "by approximation with" in formal writing?

Yes, "by approximation with" is grammatically correct. However, its suitability for formal writing depends on the context. Ensure it accurately reflects the method being described and isn't used as a substitute for more precise language when precision is required.