Accession Number:

AD0751253

Title:

Computable Error Bounds for Inner Product Evaluation,

Descriptive Note:

Corporate Author:

AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s):

Report Date:

1972-10-01

Pagination or Media Count:

22.0

Abstract:

In floating-point computations, the accurate evaluation of the inner product Ssup osub n the summation of a sub i b sub i is very important in solving linear algebraic problems. Due to round-off errors in actual computation, the computed s sub n satisfies s sub n the summation of a sub i b sub i e where e is correction necessary to make the equation hold exactly. In the paper the author gives an a posteriori bound for e which is simply the absolute sum of all intermediate computed products and sums. This bound is sharp compared with the one obtained using J. H. Wilkinsons backward approach. It can further be sharpened if chopped operations are used for the inner product. Some probabilistic considerations are also discussed together with two numerical examples. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE