Welcome to the Java Programming Forums


The professional, friendly Java community. 21,500 members and growing!


The Java Programming Forums are a community of Java programmers from all around the World. Our members have a wide range of skills and they all have one thing in common: A passion to learn and code Java. We invite beginner Java programmers right through to Java professionals to post here and share your knowledge. Become a part of the community, help others, expand your knowledge of Java and enjoy talking with like minded people. Registration is quick and best of all free. We look forward to meeting you.


>> REGISTER NOW TO START POSTING


Members have full access to the forums. Advertisements are removed for registered users.

Results 1 to 5 of 5

Thread: condition number help?

  1. #1
    Junior Member
    Join Date
    Feb 2013
    Posts
    22
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Default condition number help?

    im instructed to calculate the condition number. according to my slides is is calculated by ||A|| ||A^-1|| = condition number. what exactly is this? absolute matrix A times absolute inverse matrix A??


  2. #2
    Super Moderator Norm's Avatar
    Join Date
    May 2010
    Location
    Eastern Florida
    Posts
    21,038
    Thanks
    52
    Thanked 2,280 Times in 2,251 Posts

    Default Re: condition number help?

    Can't see where your java programming problem is here, so I moved it to the algorithms section.
    If you don't understand my answer, don't ignore it, ask a question.

  3. #3
    Junior Member
    Join Date
    Feb 2013
    Posts
    22
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Default help with matrix condition number

    im instructed to calculate the condition number. according to my slides is is calculated by ||A|| ||A^-1|| = condition number. what exactly is this? absolute matrix A times absolute inverse matrix A??

  4. #4
    Super Moderator helloworld922's Avatar
    Join Date
    Jun 2009
    Posts
    2,896
    Thanks
    23
    Thanked 619 Times in 561 Posts
    Blog Entries
    18

    Default Re: condition number help?

    That notation looks familiar, but I can't recall what it is off the top of my head. Try asking what it is over at Math Stack Exchange.

  5. #5
    Member
    Join Date
    Jun 2012
    Location
    Left Coast, USA
    Posts
    451
    My Mood
    Mellow
    Thanks
    1
    Thanked 97 Times in 88 Posts

    Default Re: help with matrix condition number

    Quote Originally Posted by gspease839 View Post
    im instructed to calculate the condition number. according to my slides is is calculated by ||A|| ||A^-1|| = condition number. what exactly is this? absolute matrix A times absolute inverse matrix A??
    The ||.|| notation means the matrix norm. You can look it up in your favorite text on linear algebra. (Or you can poke around on the web and see if you can find a description that suits your sensibilities.)

    I'll dumb-down the language from strict linear algebraic terminology:

    If the matrix is diagonalizable, it turns out that the condition number is equal to (and is "usually" calculated by) the absolute value of the eigenvalue with largest absolute value divided by the absolute value of the eigenvalue with smallest absolute value.

    If the matrix is not diagonalizable, it turns out that the condition number is equal to (and is "usually" calculated by) the absolute value of the singular value with largest absolute value divided by the absolute value of the singular value with smallest absolute value.

    The significance of the condition number of a matrix in many applications goes something like this:

    If the condition number of an invertible matrix is "close to" 1 (the eigenvalues are all of similar order of magnitude) the numerically calculated inverse of the matrix isn't terribly sensitive to small errors in the input matrix coefficients or to roundoff error in the calculations.

    One result is that solutions of systems of equations whose coefficients are the elements of matrix with this property (eigenvalues all of similar order of magnitude) can be calculated without being terribly sensitive to small errors in the input coefficients or to roundoff errors in the calculations. Such a matrix is said to be "well conditioned."

    On the other hand, if an invertible matrix has a high condition number ("lots greater than 1"), the matrix is said to be "ill-conditioned," and calculation of the inverse matrix is extremely sensitive to small input errors or roundoff errors in the calculations. Calculated solutions of systems of equations whose coefficients are elements of an ill-conditioned matrix are extremely sensitive to small input errors or roundoff errors in the calculations.


    Cheers!

    Z

Similar Threads

  1. [SOLVED] Confused on if statements condition...
    By Discoveringmypath in forum Loops & Control Statements
    Replies: 4
    Last Post: January 28th, 2013, 02:18 PM
  2. Have Problem with if condition...Please Help me...
    By Jalpesh Ruparel in forum What's Wrong With My Code?
    Replies: 1
    Last Post: April 26th, 2011, 01:54 AM
  3. Waiting until condition
    By aussiemcgr in forum Java Theory & Questions
    Replies: 1
    Last Post: October 22nd, 2010, 09:24 AM
  4. Problem with condition
    By shamed in forum What's Wrong With My Code?
    Replies: 7
    Last Post: December 7th, 2009, 03:51 PM