Why is there a difference when you Sum over an Array versus a Generator?

New to Julia
1

Vector summation:
‘’’ sum([1/n^2 for n = 1:100000])‘’’
returns: 1.644924066898228

Generator summation:
‘’‘sum((1/n^2 for n = 1:100000))’‘’
returns: 1.6449240668982423

Why is there a difference in these results, and which summation method is the most accurate?

2

https://0.30000000000000004.com/. The list version uses pairwise summation which means on average it will be slightly more accurate.

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3

Thank you. For clarification, is the list version the vector summation method (i.e. enclosed in with brackets)?

4

Yeah.

5

For an even more accurate result, sum the terms in order of increasing absolute value:

sum((1/n^2 for n = 100000:-1:1))   # returns 1.6449240668982263

or use BigFloat:

sum((1/big(n)^2 for n = 1:100000)) # returns 1.64492406689822626980574850331269185564752...
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6

if you want it accurate AND fast you may have a look at https://github.com/JuliaMath/AccurateArithmetic.jl

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