Accession Number : AD0751253

Title :   Computable Error Bounds for Inner Product Evaluation,

Corporate Author : AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Tsao,Nai-Kuan

Report Date : OCT 1972

Pagination or Media Count : 22

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)

Descriptors :   (*MATRICES(MATHEMATICS), NUMERICAL ANALYSIS), EQUATIONS, ITERATIONS, PROBABILITY DENSITY FUNCTIONS, RANDOM VARIABLES, ERRORS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE