Off-topic, but:

(not noble, sorry about missing the spell corrector blunder)

You can correct a typo in the title of a discussion you have started. Hit the Edit button below your published post. Then you can edit the title, in the input field on top.

Another comment (but this isn't really my area of expertise, so someone else may have more insight)... it looks like you've gone to a lot of trouble to define certain quanties with 50 digits of precision, but in your FindRoot calculations, you are setting WorkingPrecision to 25. Furthermore, the documentation states that AccuracyGoal and PrecisionGoal by default are set to WorkingPrecision/2. So, I think that we can only expect a dozen or so digits of precision in the results. Is that what you want?

Also, after waiting for several minutes for the final two calculations to complete, I just gave up. So I don't know what you're trying to show. Please provide a more focused and manageable example of where you're losing precision unexpectedly (sorry, but I'm just not gonna invest my whole day in this).

We could better help you if you provided some sample code that represents what you want to do. In the meantime, I'll guess that you are running into a common challenge for new Mathematica users trying to control precision. Whenever you write a number like 1.0, i.e. anytime you use a decimal point and no other precision info, you are specifying a number with machine precision (about 16 decimal digits). Once you've committed to a particular precision, you cannot expect precision to increase in subsequent calculations. Setting the working precision for a particular calculation cannot increase the precision of the quantities you feed to that calculation. So, the general strategies are to use infinite precision quantities for your inputs (things like integers or Pi) or to specify the precision of your inputs sufficiently high. One way to specify precision is with a backtick, e.g. 1.0`100 (approximately 100 digits of precision in this case). But again, we'd need a concrete example of what you're trying to do to provide more specific guidance.

Many thanks for the help and tips so far.

I have attached a Notebook which illustrates the basic problem. The key numbers that I am trying to calculate are generated in the module etaLIST and are stored in the list etas. At the end of the Notebook you can see how the precision of these data varies with the parameter l.

In my real problem, I have to sum up a series which may contain up to 15000 terms. Each term has three parts. One part is the exponent of an eta and so the precision of the final sum is critically dependent upon the accuracy and precision with which I can compute the etas themselves.

I may have gone too far with my use of backticks !!

David

Attachments:

Precision Tests.nb