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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 • 2499 views

the n-th iteration

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

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.
  • 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

the i-th iteration

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.

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.
  • 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

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