My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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????
evinda is offline  
 
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.
icemanfan is offline  
November 1st, 2013, 03:00 PM   #3
Member
 
Joined: Apr 2013

Posts: 52
Thanks: 0

Re: SOS NUMERICAL ANALYSIS

forwards: 1+....+1/(n-1)^2+1/n^2
backwars: 1/n^2+1/(n-1)^2+...+1
evinda is offline  
November 1st, 2013, 03:28 PM   #4
Global Moderator
 
CRGreathouse's Avatar
 
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.?
CRGreathouse is offline  
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..
evinda is offline  
November 1st, 2013, 06:13 PM   #6
Global Moderator
 
CRGreathouse's Avatar
 
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.
CRGreathouse is offline  
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??
evinda is offline  
November 2nd, 2013, 03:37 PM   #8
Global Moderator
 
CRGreathouse's Avatar
 
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:
Originally Posted by evinda
But it does not give better results for n<=1000..why??
It does for me. With n = 5 and 19 digits of precision, backward gives
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
CRGreathouse is offline  
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 ???
evinda is offline  
November 3rd, 2013, 08:22 AM   #10
Global Moderator
 
CRGreathouse's Avatar
 
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.
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
analysis, numerical, sos



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Numerical Analysis Faith Real Analysis 1 July 7th, 2014 04:33 AM
Numerical analysis problem darkark Applied Math 1 June 17th, 2013 05:32 PM
Analysis of Image superimposing using numerical analysis saugata bose Computer Science 0 March 8th, 2013 11:03 AM
Numerical Analysis Problem help!! wale06 Applied Math 0 October 24th, 2011 04:54 PM
I need help with a problem : Numerical Analysis fluidistic Applied Math 5 April 26th, 2008 04:43 PM





Copyright © 2019 My Math Forum. All rights reserved.