ERROR VARIANCE ANALYSIS OF FLOATING POINT DOT PRODUCT COMPUTATIONS
V. Sathe, Palghat P. Vaidyanathan · 2005
Iht prodiict computatioii of two vectors x and y) and evaluation of l2-norm or energy (square of the l?-iiorm) of a vector x are two basic computational steps ill a variety of signal processing algorithms. Xigoritltiiis like the QR algorithm and the fast ItLS algorithm make a repetitive use of these steps. Turnerical analysis of these two computational steps for t,hc fioating point number system is available iii literature in terins of bounds on the masiiitum error incurred in (.lie computation. In this paper, we atid ii stati-it.ica1 flavor to siicli tiin aiiidysis. For tlic two coiiii’utiitioii;il steps iiientioiied above, we derive expressions for the error lwiaiices assuming an appropriate probability of distribution for tlie entries of tlie vectors x and y. The expressions simplify for the particular case of Gaussian probability distribution. \Ye also conipiire these resiilts with the corrosponilitig resiil~s for 51 iisctl point nuiiiber system. X cornpari-,,n of tlie theory ~vitli simulations is also included.