I was reading about error analysis in numerical methods, particularly about calculating the sum of arrays. I understand how naively summing all elements can lead to accumulation of error especially when the number of elements is very large and all elements are of small order. In the alternative algorithms, the source explains the Kahan algorithm where an approximation of error is defined as ((a+b)-a)-b. They go on to state "subtraction operations are better conditioned since moving from large numbers to small ones adds digits of precision due to cancellation"
So my questions are: 1. What do you mean by well-conditioned operations? I understand the meaning of well-conditioned problems in terms of forward and backward error but not well-conditioned operations.
- Intuitively subtraction and addition appear to me to be equally prone to errors as the magnitudes of the two operands matter in both cases.
Could someone please explain the meaning of the statement and whether my understanding is correct or flawed? Thanks in advance