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Abstract
En 中文
In this article, we combine recursive summation techniques with Kahan-Babuska type balancing strategies [ 1], [ 7] to get highly accurate summation formulas. An i-th algorithm have only O(n(log(2)(n)epsilon)(i+1)) error beyond 1upl and thus allows to sum many millions of numbers with high accuracy. The additional afford is a small multiple of the naive summation. In addition we show that these algorithms could be modified to provide tight upper and lower bounds for use with interval arithmetic.
Keywords:
floating-point numbers
rounding errors
summation algorithm
interval arithmetic
Journal
C
IF:
2.8
Papers:
2.3K
Citations:
3.5K
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