November 1st, 2013, 08:44 AM  #1 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  SOS NUMERICAL ANALYSIS
I noticed at a program that is calculating the sum ,that for n<10000 the forward method is better,and for n>=10000,the backward method is better..Why does this happen???? 
November 1st, 2013, 11:19 AM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: SOS NUMERICAL ANALYSIS
To answer that question, we would have to know how the program is calculating the sum.

November 1st, 2013, 03:00 PM  #3 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  Re: SOS NUMERICAL ANALYSIS
forwards: 1+....+1/(n1)^2+1/n^2 backwars: 1/n^2+1/(n1)^2+...+1 
November 1st, 2013, 03:28 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: SOS NUMERICAL ANALYSIS
What program? What (hardware) architecture? What precision (or is this done in rational arithmetic)? How do you decide "better": speed, higher accuracy, etc.?

November 1st, 2013, 03:44 PM  #5 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  Re: SOS NUMERICAL ANALYSIS
The program should approximate pi..Also,it uses floats.I look how near the result approximates pi,to decide which way(backward/forward) is better..

November 1st, 2013, 06:13 PM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: SOS NUMERICAL ANALYSIS
Backward should give better answers then, regardless of the size. Speed shouldn't vary much.

November 2nd, 2013, 03:48 AM  #7 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  Re: SOS NUMERICAL ANALYSIS
But it does not give better results for n<=1000..why??

November 2nd, 2013, 03:37 PM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: SOS NUMERICAL ANALYSIS Quote:
1.6429360655148941[color=#FF0000]70[/color] while forward gives 1.6429360655148941[color=#FF0000]42[/color] and the correct result is 1.6429360655148941[color=#FF0000]69[/color]802  
November 3rd, 2013, 07:54 AM  #9 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  Re: SOS NUMERICAL ANALYSIS
Did you find the approximation of pi or of (pi^2)/6 ??? 
November 3rd, 2013, 08:22 AM  #10 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: SOS NUMERICAL ANALYSIS
I found the sum 1 + 1/4 + 1/9 + ... + 1/n^2.


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