High-accuracy arithmetic software—some tests of the ACRITH problem-solving routines
ACM Transactions on Mathematical Software (TOMS) - The MIT Press scientific computation series
The FUNPACK Package of Special Function Subroutines
ACM Transactions on Mathematical Software (TOMS)
Choice of Basis for Chebyshev Approximation
ACM Transactions on Mathematical Software (TOMS)
Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
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J. H. Wilkinson, in justifying backward error analyses, advanced the proposition that a numerical routine could not be blamed if the computed answer was the exact answer to the problem with slightly perturbed input. Such a model was established by Wilkinson (1968) for the solution of linear equations, ns by (I) Gaussian elimination and (II) triangular decomposition using double precision accumulation of inner products. In the latter it is usual that inputs are perturbed only by a small multiple of a unit rounding error (see formula (175)).