the n-th iteration vs the i-th iteration

Both phrases are correct, but they are used in different contexts. "The n-th iteration" is commonly used in mathematics, computer science, and engineering to refer to a specific iteration in a sequence, where 'n' represents any integer. On the other hand, "the i-th iteration" is also correct and is commonly used in mathematical contexts, where 'i' is often used as a variable to represent an index or iteration number.

Last updated: March 19, 2024 • 2649 views

This phrase is correct and commonly used in mathematics, computer science, and engineering to refer to a specific iteration in a sequence.

"the n-th iteration "

This phrase is used to refer to a specific iteration in a sequence, where 'n' represents any integer. It is commonly used in mathematical contexts.

Examples:

In the n-th iteration of the algorithm, the error rate decreased significantly.
Please refer to the n-th iteration of the loop for further details.

Show examples from the web [+]

The second degree terminated Taylor expansion about xn is. where is the error at the n-th iteration and . Since , we find. But, by the Newton-Raphson formula,.
The total area covered at the nth iteration is : \begin{align}A_{n} & = \frac{1}. While the total length of the perimeter is : \begin{align}P_{n} & = 4 \left(\ ...
On the n-th iteration: calculate q_n with the Arnoldi method;; find the y_n which minimizes ||rn||;; compute x_n = Q_n y_n ;; repeat if the residual is not yet small ...
Apr 8, 2015 ... When you're on the n'th iteration of your loop, why do you think ID(n+1) will have a value yet? You have not assigned a value to that element ...

Alternatives:

the nth iteration
the n-th step
the n-th cycle
the n-th round
the n-th phase

This phrase is correct and commonly used in mathematical contexts, where 'i' is often used as a variable to represent an index or iteration number.

"the i-th iteration "

This phrase is used in mathematical contexts to refer to a specific iteration, where 'i' is typically used as a variable to represent an index or iteration number.

Examples:

Let's consider the i-th iteration of the sequence.
In the i-th iteration of the algorithm, the convergence was achieved.

Show examples from the web [+]

Pro: The error of the i+1th iteration is roughly proportional to the square of the error of the ith iteration - this is called quadratic convergence; Con: Some functions ...
During the i-th iteration this call returns i-1. If EPSSolve() is complete, then parameter "its" contains either the iteration number at which convergence was ...
Normally used is = 0.001 %tol : tolerance value, normally used is = 1e-9 %n : number of iterations %i : the i-th iteration when root found within tol level %err ...
At the \(i\)-th iteration, clusters with indices Z[i, 0] and Z[i, 1] are combined to form cluster \(n + i\). A cluster with an index less than \(n\) corresponds to one of the ...

Alternatives:

the ith iteration
the i-th step
the i-th cycle
the i-th round
the i-th phase

How TextRanch works

Fast and reliable proofreading, editing, and language advice tailored to your needs.

1. Choose Your Service

Quick Text Editing

Emails and short texts
Proofreading & editing
Ready in 5-10 minutes

SUBMIT YOUR TEXT NOW

Document Editing

Documents of any type (*.docx)
Advanced & Premium editing
Ready in as little as 4 hours

UPLOAD YOUR DOCUMENT

Ask an Editor

Personalized answers to your language questions
Expert guidance on grammar, style, and usage
Ready in 24 hours

ASK YOUR QUESTION

Upload your document or paste your text directly into our platform. Your text is reviewed and refined by our expert editors (real people, not machines) who understand the nuances of English. Expect corrections, improvements, and insightful suggestions that enhance the clarity, tone, and professionalism of your writing.

3. Receive Your Polished Text

In just a few minutes (or hours for longer documents), you'll receive your corrected text. Review the changes, make any final adjustments, and confidently share your polished English with the world.
You can count on a personalized, friendly service every time you use TextRanch. We're committed to helping you make a great impression with every word you write.

We proofread and edit these types of texts and documents:

Short texts Business Emails Personal Emails Social media posts Resume and Curriculum Vitae Business documents Sales proposal Research and academic papers Thesis Dissertation Essays Articles Blog posts and much more....

Why choose TextRanch?

Complete Privacy

Your texts are safe and secure with us. We never share your information with third parties.

Affordable Pricing

No subscription fees and rates up to 50% cheaper than other online editing services.

100% Satisfaction

We guarantee that you'll be satisfied with the quality of our service or your money back.

Top Customer Service

Our team is here to help you with any questions you may have. Contact us anytime.

Our Customers Love Us!

We have an average rating of 4.79 stars based on 283125 votes, and

4.9 Excellent - Reviews 2.137

"7 years without any disappointment. Always 100% satisfied. You guys are the best in the world at what you do. Thank you so much :)"

Zubair
from Bangladesh

"I wasn't aware of this service, it's fascinating and more reliable than standard IA tools available on the internet"

Arturo
from Mexico

"In a world of text messages and online communication, this is great to have as a live tool. Thank you."

Selena
from USA

"Wow, it's just so excellent. I never would have believed I could have a sure and excellent English companion. Thanks, TextRanch."

Ifiok
from Nigeria

"This is my first time using TextRanch, and I like how the editors take time to correct my text. To everyone who has never used TextRanch before, I highly recommend trying it."

Wilson
from France

"It is an amazing source of feedback because, as a non-native speaker, I really need to have a reliable helper correct my text."

Susan
from Germany

the n-th iteration vs the i-th iteration