What is meant by this statement?

  • Context: Graduate 
  • Thread starter Thread starter Amany Gouda
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of a statement regarding the stopping criteria for iterative numerical methods, specifically the Successive Over-Relaxation (SOR) method and Gaussian elimination (GE). The focus is on understanding the Euclidean norm of the residual vector and its implications for the convergence of these methods.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests stopping the iteration when the Euclidean norm of the residual vector between the SOR solution and the GE solution is less than 1.0e-5.
  • Another participant defines the Euclidean norm of a vector and requests clarification on what the SOR and GE solutions are.
  • A subsequent post reiterates the definition of the Euclidean norm and provides definitions for SOR and GE, indicating that SOR refers to the successive over-relaxation method and GE to Gaussian elimination with partial pivoting.
  • One participant summarizes the initial statement by suggesting that it means to run both numerical approximations simultaneously and stop when the difference between the two solutions is less than 0.00001.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the original statement, with some seeking clarification on the methods involved. There is no consensus on the interpretation of the stopping criteria, as the discussion includes requests for more details and definitions.

Contextual Notes

Some assumptions about the definitions and applications of the SOR and GE methods may be missing, and the discussion does not resolve the implications of the stated stopping criteria.

Amany Gouda
Messages
29
Reaction score
0
stop the iteration when Euclid norm of the residual
vector between SOR solution and GE solution becomes less than
1.0e-5
 
Physics news on Phys.org
The Euclidean norm of a vector ##\mathbf x=(x_1,\dots,x_n)## is denoted by ##|\mathbf x|## and defined by
$$|\mathbf x| =\sqrt{(x_1)^2+\cdots+(x_n)^2}.$$ If you want more help, you will have to provide more details. What is the SOR solution and the GE solution?
 
  • Like
Likes   Reactions: perplexabot
Fredrik said:
The Euclidean norm of a vector ##\mathbf x=(x_1,\dots,x_n)## is denoted by ##|\mathbf x|## and defined by
$$|\mathbf x| =\sqrt{(x_1)^2+\cdots+(x_n)^2}.$$ If you want more help, you will have to provide more details. What is the SOR solution and the GE solution?
thank you for replying;
SOR is : successive over-relaxation method.
GE: Gaussian elimination with partial pivoting
 
Then what it says is "run two numerical approximations, the "SOR" and "GE", simultaneously. Stop when the difference between the two solutions is less than 0.00001."
 
  • Like
Likes   Reactions: perplexabot

Similar threads

Undergrad A true or false statement concerning condition number of a matrix
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Large is the Residual Error in FEA Solutions of PDEs?
  • · Replies 12 ·
Replies
12
Views
3K
The Convergence Of SOR iteration method
  • · Replies 2 ·
Replies
2
Views
2K
MHB Check the statements about a 4x5 matrix with rank 2.
  • · Replies 9 ·
Replies
9
Views
5K
High School Parametric Representation of Lines
  • · Replies 13 ·
Replies
13
Views
4K
Graduate What Iterative Method is This?
  • · Replies 15 ·
Replies
15
Views
3K
Solving for ##x## for a given inequality
  • · Replies 3 ·
Replies
3
Views
2K
Graduate What is meant by can be identified with
  • · Replies 2 ·
Replies
2
Views
5K
Comp Sci Genetic algorithm knapsack problem
  • · Replies 1 ·
Replies
1
Views
2K
How Do You Find the Inverse of 5 in Z12?
  • · Replies 12 ·
Replies
12
Views
2K