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Avoiding recursion during sequence alignments offers advantages for speed and in-process resources.
If one chooses a small parameter such that it guarantees the convergence of the iterative sequence, the recursion leads to slow speed of convergence.
It would be harder to use this to turn equation (4) into the definition of two sequences by recursion.[3] The upshot is that we can start to see some kind of difference when we use one kind of representation instead of another.
We propose a regularized, pseudo-dynamical recursion scheme that provides a sequence of updates, which are almost insensitive to the regularizing term as well as the time step size used for integrating the pseudo-dynamical form.
The sequence of the recursion formula (2.1) is called the Picard sequence.
A small τ n guarantees the convergence of the iterative sequence, but the recursion leads to slow speed of convergence.
Let (S_{n}) be an rth-order linear recurrence sequence satisfying the recursion (S_{n+r}=sum_{k=0}^{r-1}c_{k}S_{n+k} ).
Recall also that the implicit midpoint rule (IMR) [13] generates a sequence by the recursion process (2.3).
In particular, Korpelevich's extragradient method which was introduced by Korpelevič [4] in 1976 generates a sequence via the recursion (12).
PGM generates an iterative sequence by the recursion x 1 ∈ C and x n + 1 = P C [ ( I − μ F ) x n ], n ≥ 1. (1.4).
PGM generates an iterative sequence by the recursion x_{1}in C quad mbox{and}quad {x_{n + 1}} = {P_{C}}bigl[(I - mu F {x_{n}}bigr].
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