its convergence to

USAGE SUMMARY

The phrase "its convergence to" is correct and usable in written English.
You can use it when discussing the approach of a sequence, function, or series towards a specific value or limit. Example: "The study focuses on its convergence to the expected outcome as the sample size increases."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

19 human-written examples

In[16], we reformulated this game as a Variational Inequality[17] and we applied the iterative gradient projection algorithm to solve it, deriving sufficient conditions for its convergence to a Nash Equilibrium (NE).

EURASIP Journal on Wireless Communications and Networking

Then, we design a powerful iterative algorithm to solve the L1-norm optimal problems, and it is easy to implement and its convergence to an optimum solution is theoretically ensured.

Pattern Recognition

The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.

Mathematical Biosciences

Its convergence to the globally optimum result can be guaranteed under under some conditions, e.g., convex utility/cost function.

EURASIP Journal on Advances in Signal Processing

For a fixed channel its convergence to the WF has been studied in [6, 7] (see also the references therein).

EURASIP Journal on Advances in Signal Processing

Besides, its convergence to the no-regret control is discussed together with the optimality system describing the no-regret control.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

41 human-written examples

Specially designed linear-rotation test equipment was built, and the experimental results showed its fast convergence to actual values in addition to its excellent responses.

Control Engineering Practice

However, it lacks internal memory which may lead to its premature convergence to local optima.

Expert Systems with Applications

Section 3 is devoted to the proof of its global convergence to a solution of EP f, C).

Journal of Inequalities and Applications

It is shown that the main drawback of the proposed approach is its possible convergence to local maxima.

EURASIP Journal on Advances in Signal Processing

In Section 2, we construct a monotone iterative scheme and establish its geometrical convergence to the solution of VI (1.4).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using the phrase "its convergence to", ensure that the subject you're discussing has a clear target or endpoint it is approaching. Provide context about what this target represents.

Common error

Avoid using "its convergence to" when the subject doesn't have a well-defined goal or limit. This phrase implies a specific endpoint, so using it vaguely can confuse your reader.

Linguistic Context

The phrase "its convergence to" functions as a noun phrase followed by a preposition, describing the act or process of approaching a limit, solution, or specific state. Ludwig AI confirms its grammatical correctness and common usage in academic and scientific writing.

Expression frequency: Common

Frequent in

Science

94%

News & Media

3%

Formal & Business

3%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "its convergence to" is a grammatically correct and commonly used phrase, as confirmed by Ludwig AI, primarily employed in formal and scientific contexts. It describes the act of something approaching a particular state, solution, or limit. When using this phrase, ensure that the target of the convergence is clearly defined to avoid ambiguity. Alternatives such as "its approach to" or "its tendency towards" can be used for slight variations in meaning. The phrase's frequency and authoritative sources indicate its reliability and appropriateness in academic and scientific writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

its approach to

Focuses on the act of nearing or coming closer, rather than the final state of reaching a limit.

its tendency towards

Emphasizes a predisposition or inclination toward a particular outcome, rather than a guaranteed result.

its movement toward

Highlights the dynamic process of changing position or state in the direction of something.

its progression to

Suggests a step-by-step advancement or development leading to a particular result.

its evolution toward

Implies a gradual development or transformation in the direction of a specific form or state.

its drift toward

Conveys a sense of gradual and often unintentional movement towards a specific condition.

its asymptotic approach to

Specifically describes approaching a limit without necessarily reaching it, often in a mathematical context.

its adherence to

Emphasizes sticking firmly to a principle, plan, or belief, showing semantic difference from the original phrase.

its conformity to

Highlights aligning or complying with a standard or norm.

its coming together at

Suggests a union or merging at a specific point, differing from a general approach.

FAQs

How do I use "its convergence to" in a sentence?

Use "its convergence to" when describing how something gradually approaches a specific value, state, or solution. For example, "The algorithm demonstrates "its convergence to" the optimal solution after several iterations."

What phrases are similar to "its convergence to"?

Similar phrases include "its approach to", "its tendency towards", or "its movement toward", which all convey the idea of something moving closer to a particular point or state.

Is it always necessary to specify what something is converging to when using "its convergence to"?

Yes, it's crucial to specify the target of the convergence. Saying simply "its convergence" is incomplete; the phrase requires a destination or goal to be meaningful. For instance, ""its convergence to" equilibrium" is more informative than just "its convergence".

Can "its convergence to" be used in non-mathematical contexts?

Yes, while often used in mathematics and science, ""its convergence to"" can be used in other contexts to describe a gradual alignment or approximation. For example, ""its convergence to" the intended design" describes refinement towards a specific goal.