Best “ordering” for floating-point addition
ACM Transactions on Mathematical Software (TOMS)
The accuracy of floating point summation
SIAM Journal on Scientific Computing
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Large-scale addition of machine real numbers: accuracy estimates
Theoretical Computer Science - Special issue on real numbers and computers
Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]
ACM Transactions on Mathematical Software (TOMS)
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
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
ACM Transactions on Mathematical Software (TOMS)
Improving accuracy for matrix multiplications on GPUs
Scientific Programming
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The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of "Cascading Accumulators" is the fastest of several methods. The Double Compensation method (in both single and double precision versions) is also perfectly accurate in all the tests performed. Although slower than the Cascade method, it is recommended when double precision accuracy is required. C programs that implement both these methods are available in the BULLETIN online repository.