alexSanchStern

3 ms·

1. 1.▲
   by alexSanchStern 11y ago

   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 can give you 128
2. 2.▲
   by alexSanchStern 11y ago

   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 you have streaming data
3. 3.▲
   by alexSanchStern 11y ago

   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 loss of a