Help with article choice

[Anton Shepelev]

[cross-posted to alt.sci.physics and alt.english.usage]

Hello, all.

I have a small question about a phrase in the abstract for a
sciences article I am co-writing:

The new method was compared to a numerical calculation
with discretization chosen sufficiently fine.

I myself would simply say: "with a sufficiently fine
discretization," but for undisclosed and absurd reasons we
must use a verb with respect to selecting a discretization.
I ask whether in the sentence above `discretization' requires
an article, and if does, then which one.

[Opinicus]

On Mon, 4 Sep 2023 13:10:16 +0300, Anton Shepelev

Post by Anton Shepelev
The new method was compared to a numerical calculation
with discretization chosen sufficiently fine.
I myself would simply say: "with a sufficiently fine
discretization," but for undisclosed and absurd reasons we
must use a verb with respect to selecting a discretization.
I ask whether in the sentence above `discretization' requires
an article, and if does, then which one.

I would say leave it as it is: that is, no article. I can see a case
for "a" as a close second and "the" as a distant third however.

Google fetches up no instances of any of the three phrases exactly.

[Anton Shepelev]

Post by Opinicus

Post by Anton Shepelev
I have a small question about a phrase in the abstract
The new method was compared to a numerical
calculation with discretization chosen sufficiently
fine.
[...]
I ask whether in the sentence above `discretization'
requires an article, and if does, then which one.

I would say leave it as it is: that is, no article. I can
see a case for "a" as a close second and "the" as a
distant third however.

And my rating is the/zero/a. My rationale for the definite
article is that a numerical method implies a discretisation,
so that we can only choose its form and finess. Similarly,
one might speak of a car with the engine replaced.

Post by Opinicus
Google fetches up no instances of any of the three phrases
exactly.

Indeed, but now I have found this:

Mangasarian has studied the convergence of the
generalized Newton method as applied to the unconstrained
minimization of a convex piecewise quadratic function of
this type with the step size chosen by the Armijo rule.