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Larger error on specific points #12
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Thanks. This is bad behavior. |
By changing the order of the integration scheme here EDIT: with the following function test_quadgk()
xgrid=-(0:0.01:2).^0.125;
y1=mittleff.(0.125,1,xgrid);
y2=mittleff_series.(BigFloat(0.125),1,xgrid,1000);
diffs = abs.(y1 .- y2)
return extrema(diffs)
end and |
This commit jlapeyre@352c2a0 decreases the error in your examples. |
I was using this package to benchmark another algorithm I'm developing and I found something weird.
I evaluated
mittleff(0.125, -x^0.125)
wherex in 0:0.01:2
. The function gives1e-15
accuracy uniformly except for some points where the errors suddenly jump by magnitudes.I wrote up a naive implementation using the infinite series and the results show that the errors come from this package rather than my algorithm.
first make sure this method converges:
then compare with MittagLeffler.jl:
you can see the last 3 digits are wrong. Surely this is still pretty accurate, but it's unexpectedly worse than what we would expect from other points:
You can see the two spikes from the plot.
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