Computable Error Bounds for Inner Product Evaluation,
Abstract
In floating-point computations, the accurate evaluation of the inner product S(sup o)(sub 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. Wilkinson's 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1972
- Accession Number
- AD0751253
Entities
People
- Nai-kuan Tsao
Organizations
- Air Force Research Laboratory