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Extra info for Advances in Computers, Vol. 3
15) + + + - Fn+k-l + hfn+k. 16) and assume as before that E(9n) = vP(zn),V(vn)= ~zQ(z,)and that the en, qn are mutually independent. 17) where M, N , R, S are again obtained as solutions of certain differential equations. Thus both the expected value and the standard deviation of the accumulated round-off error are improved by a factor of the order of h in the summed method. 10) is typical. , about p , y, P, Q and the constants p, v, u, T . For fixed point operations and symmetric rounding and assuming uniform distribuof tion between the limits -u/2 and u/2 where u denotes the basic unitthe machine, the distributions are p = P = 0, y = Q = 1, u = T = u / d 1 2 .
About p , y, P, Q and the constants p, v, u, T . For fixed point operations and symmetric rounding and assuming uniform distribuof tion between the limits -u/2 and u/2 where u denotes the basic unitthe machine, the distributions are p = P = 0, y = Q = 1, u = T = u / d 1 2 . Some experiments on some simple equations show that quite accurate predictions of the distribution of accumulated round-off error can be made. Experiments applied specifically to the equations for the n-body problem are currently being conducted a t Space Technology Laboratories, Inc.
Another procedure is to examine the magnitude of the attractions acting on the vehicle-for example, the distance from the earth might be one simple criterion-and choose the interval on the basis of experience. When integrations are performed over a great many time steps, the accumulation of round-off errors can lead to very serious degradation in the accuracy of the results. A very simple, effective, and inexpensive method for reducing accumulated round-off error in any numerical integration method is that of double precision accumulations.