On the distributions of significant digits and roundoff errors
Communications of the ACM
A comparison of floating point summation methods
Communications of the ACM
Accurate floating-point summation
Communications of the ACM
On accurate floating-point summation
Communications of the ACM
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Reducing truncation errors by programming
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
More accuracy at fixed precision
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
A comparison of methods for accurate summation
ACM SIGSAM Bulletin
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This correspondence examines the influence of the summation order on the numerical accuracy of the resulting sum when the addition is performed using floating-point, finite-precision arithmetic. A simple statistical model is used to find the relative performance of various addition procedures. It is shown that phrasing the question in terms of finding a best ordering is overly restrictive since the most natural and accurate procedures for performing the addition utilize the storage of intermediate sums as well as performing orderings.