CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Conditional number

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   June 15, 2001, 04:26
Default Conditional number
  #1
pawel
Guest
 
Posts: n/a
I have a silly question: how to calculate the conditional number of a matrix? I should know it myself, but I graduated a few years ago and I have completly forgotten some basic facts.

Pawel
  Reply With Quote

Old   June 15, 2001, 05:19
Default Re: Conditional number
  #2
Praveen Chandrashekar
Guest
 
Posts: n/a
condition number of square matrix A = ||A|| ||inv(A)||

where ||.|| is some matrix norm and inv(A) is the matrix inverse of A. If you use one particular norm, which I dont recall at the moment, the condition number takes a simple form,

cond(A) = max |eigenvalue| / min |eigenvalue|

  Reply With Quote

Old   June 15, 2001, 11:48
Default Re: Conditional number
  #3
kalyan
Guest
 
Posts: n/a
I think the norm you are refering to is the L2 norm. Condition numbers for matrices resulting from discretization of standard operators like the Laplacian can be easily estimated. Estimation of condition numbers for more general matrices requires numerical algorithms.
  Reply With Quote

Old   June 17, 2001, 14:07
Default Re: Conditional number
  #4
clifford bradford
Guest
 
Posts: n/a
that's the one I'm familiar with. It's essentially the stiffness if the system.
  Reply With Quote

Old   June 18, 2001, 06:02
Default Re: Conditional number
  #5
Sebastien Perron
Guest
 
Posts: n/a
The norm of a matrice is the product || A || * || A^-1 || where || .. || is a norm such as:

1) || A ||_1 = max(j) sum_i (a_ij)

2) || A ||_2 = sqrt( rho(A^t A ) ) where rho(A^t A ) is the spectral radius of A^t*A

3) || A ||_inf = max(i) sum_j( |a_ij| )

or when the matrix is symetric the condition number is given by:

max( | lambda_i |) / min ( | lambda_i | ) where lambda are the eigenvalues of A.

  Reply With Quote

Old   June 18, 2001, 09:30
Default Re: Conditional number
  #6
Atit Koonsrisuk
Guest
 
Posts: n/a
If I have Ax=b, when will I have to find the conditional number? and what is the physical meaning of conditional number and the spectral radius? Thank you very much.

Atit Koonsrisuk
  Reply With Quote

Old   June 18, 2001, 17:01
Default Re: Conditional number
  #7
Sebastien Perron
Guest
 
Posts: n/a
In real life, You seldom (never) have to compute the condition number. For some systems, such as the discretization of a poisson type equation, the condition number can directly computed (or estimated) from known expressions.

The condition number estimates the effect of small perturbations on the B vector or the coefficients of the matrix A will have the solution. When the condition number is high, the small perturbations will cause big change on the solution. (this is the case for poisson type equations).

The spectral radius is the lagest eigenvalue of the matrix.
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Mesh Refinement Luiz Eduardo Bittencourt Sampaio (Sampaio) OpenFOAM Mesh Utilities 41 January 17, 2013 03:43
DecomposePar unequal number of shared faces maka OpenFOAM Pre-Processing 6 August 12, 2010 09:01
BlockMeshmergePatchPairs hjasak OpenFOAM Native Meshers: blockMesh 11 August 15, 2008 07:36
Unaligned accesses on IA64 andre OpenFOAM 5 June 23, 2008 10:37
Trimmed cell and embedded refinement mesh conversion issues michele OpenFOAM Other Meshers: ICEM, Star, Ansys, Pointwise, GridPro, Ansa, ... 2 July 15, 2005 04:15


All times are GMT -4. The time now is 07:00.