N
Calculate SN =∑ 19 .
i=1
You should use math.sqrt(19.0) for the value of 19.
Calculate SN using the two methods we discussed in class, naive summation and compensated summation. Perform the
summations for N = 10 ,10 ,10 ,10 ,10 , and 10 . If the 3 4 5 6 7 8 summations for 10 take more than an hour, you can skip8 those.
Calculate the time of each summation using code such as start_time = time.time() end_time = time.time() elapsed_time = end_time − start_time
Calculate the "exact" value of the sum using the expression S%N =N *math.sqrt(19.0)
For each of the SN that you calculate, determine the absolute and relative errors of the results. Present your results (including the timing of your calculations) in a table.
Analyse you results as thoroughtly as you can and discuss them. Are these errors consistent with the expressions for errors that we discussed in class and that are in the posted classroom presentations? How do the speeds of the two methods compare?
