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 SN =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?
Include all of your analysis and discussion in your .ipynb file and submit the file through Blackboard. The name of the file you submit should be lastname_firstname_AS02.ipynb.
Do not clear your results after your last run so that I will be able to see your results without rerunning your file.
If you collaborate with anyone on this assignment, be sure to follow the collaboration guidelines in the syllabus.
