Some a Posteriori Error Bounds in Floating-Point Computations

Authors:
Nai-kuan Tsao
Affiliations:
Applied Mathematics Research Laboratory, Aerospace Research Laboratories, Wright-Patterson AFB, Dayton, Ohio
Venue:
Journal of the ACM (JACM)
Year:
1974

Citing 5
Cited 0

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Abstract

Efficiently computable a posteriori error bounds are attained by using a posteriori models for bounding roundoff errors in the basic floating-point operations. Forward error bounds are found for inner product and polynomial evaluations. An analysis of the Crout algorithm in solving systems of linear algebraic equations leads to sharper backward a posteriori bounds. The results in the analysis of the iterative refinement give bounds useful in estimating the rate of convergence. Some numerical experiments are included.