Even when summing using doubles, you can lose precision. In general, Kahan summation allows you to double the intermediary precision of your sums, so if you're losing precision even with 64-bit doubles, Kahan summation…
Pairwise summation is definitely a useful technique, depending on your situation. However, it does have the key limitation that you need to have all your data beforehand. There are quite a few cases in practice where…
Yes, that's completely true. But while there are still inputs for which terrible accuracy could result, for many of the inputs which would arise in practice, the Kahan summation technique is "good enough" to prevent…
Even when summing using doubles, you can lose precision. In general, Kahan summation allows you to double the intermediary precision of your sums, so if you're losing precision even with 64-bit doubles, Kahan summation…
Pairwise summation is definitely a useful technique, depending on your situation. However, it does have the key limitation that you need to have all your data beforehand. There are quite a few cases in practice where…
Yes, that's completely true. But while there are still inputs for which terrible accuracy could result, for many of the inputs which would arise in practice, the Kahan summation technique is "good enough" to prevent…