"The selection of these points is usually determined by the degree of accuracy required, but is arbitrary in other respects."

I may be wrong in how I'm hearing "степень точности решения задачи", but isn't there a nuance here? If you write only "determined by the accuracy", then it could be understood as either 1) how accurate you are will determine what points you come up with, or 2) how you select the points will depend on how accurate you are required to be. Since it seemed to me to mean the second choice, I added "required". If the sense is 1), I would take out "required".






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Note added at 5 hrs (2009-10-06 13:16:16 GMT)
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In reply to asker's note:

Then I would keep "required", or even expand it to "required in the solution", or, if the style is more casual, "by how accurate the solution needs to be".