Issue No.07 - July (1977 vol.26)
G. Bohlender , Institute of Applied Mathematics, University of Karlsruhe
Algorithms are given that compute multiple sums and products and arbitrary roots of floating-point numbers with maximum accuracy, The summation algorithm can be applied to compute scalar products, matrix products, etc. For all these functions, simple error formulas and the smallest floating-point intervals containing the exact result can be obtained.
Accuracy, errors, floating-point computations, multiple-length mantissas, roots of floating-point numbers, rounding.
G. Bohlender, "Floating-Point Computation of Functions with Maximum Accuracy", IEEE Transactions on Computers, vol.26, no. 7, pp. 621-632, July 1977, doi:10.1109/TC.1977.1674894