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Handling Singular matrices in Algorithms

  1. Mar 28, 2005 #1
    Hi All

    I'm new to this forum so please be kind :)

    I am doing a project on handling singular matrices in algorithms.

    Basically what i have to do is to find out how to solve the system Ax=B when A is not square or det(A)=0. Because it does not have an inverse, I dont know what to do or how to approach this problem. Any help would be appreciated


    P.S I tried the Guassian Elimination Method, but I have to find another way
     
  2. jcsd
  3. Mar 28, 2005 #2

    SpaceTiger

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    What was wrong with gaussian elimination? I had a similar problem a while back (specifically, I needed to do it numerically) and I finally settled on writing a gaussian elimination routine.
     
  4. Mar 28, 2005 #3

    Hurkyl

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    You could apply some sort of regularization. e.g. instead solve:

    [tex]
    (A^T A + \lambda I) x = A^T b
    [/tex]

    (for your favorite λ > 0)

    The system is no longer singular, but the answers you get will be biased away from the actual solutions. In particular, the answer will be unique, instead of getting a bunch of solutions.


    I don't think this would help with Gaussian elimination, though. I share SpaceTiger's question -- what's wrong with it?
     
  5. Mar 30, 2005 #4
    Thanx Guys,

    I really appreciated your help. Nothings wrong with the gaussian elimination method. I just have to find out "various" ways of solving the system and tha Gaussian Elimination is just another method.

    I have another question. Consider A , an n*n matrix which is invertible, and A^-1, its inverse. If A is transposed, how would it affect A^-1. (in other words how can i find the inverse of the Transpose of A without solving [A|I])

    Thanx in advence
     
  6. Mar 30, 2005 #5
    Look up Rank-Deficient Least Squares methods.
     
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