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How to set precision and accuracy correctly

Posted 10 years ago

Hello, again. I have been working a particular calculation on and off for six months. It has been one step forward and one step back. The group has been helpful, but when I begin to dig a bit deeper, the help runs out of steam.

I have a parametric function that, with certain WorkingPrecision, AccuracyGoal, and PrecisionGoal settings, throws off a smooth plot using Plot. Increasing the accuracy and precision parameters changes the plot, sometimes showing a breakup of the smooth curve. Even more increases in the precision parameters never completes the calculations.

I am normalizing a numerical integral with a straight integral over the same range, so I cannot set up the various precision variables in that part of the equation. None the less, for purposes of speed...which for these calculations can be up to an hour...I keep the straight Integral normalization rather than a numerical integral, and I have checked that they both throw off the same values over the expected parameter ranges.

However, when I look at just the first point in the plot, the value can be larger than in Plot. When I perform a ListPlot of the Table for the function, I get the first terms to be greater relative to the value from Plot. When I increase the various precision parameters, the plot begins to fragment and then with more increases does not run to completion.

My hunch is that I am getting the correct values in Table and ListPlot at the beginning of the calculations before the data breaks up, and by breaking up I mean step functions. Trouble is that the step functions begin a new smooth plot that follows the curve of the lower precision calculations.

I am stumped. What are the correct values? How does increasing the required precision and accuracy introduce "noise" or discontinuities? Better yet, when I reduce the parameter settings and get a "smooth" curve, how can I be sure I am not getting incorrect values?

Along these same lines, I believe I read a post in which there was a way to embed plots with several parametric parameters being processed, something like embedded do-loops. It was not the same as loading the Plot argument with multiple functions being plotted over the same parameter but appeared to be a sequential plot with a second parameter being indexed over a range. Does that ring a bell?

POSTED BY: Luther Nayhm
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