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Why is there a second pivot?

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Use LU factorization with partial pivoting for the following set of equations:

    3x1 - 2x2 + x3 = -10
    2x1 + 6x2 - 4x3 = 44
    -8x1 - 2x2 + 5x3 = -26


    3. The attempt at a solution
    I made an attempt to solve this problem, but my answer was wrong compared to the book. There was an additional partial pivot after setting elements 21 & 31 equal to zero. I just would like to know why?

    The following is what I got for my L and U matrices:

    U=
    [ -8 -2 5 ]
    [ 0 5.5 -3.25]
    [ 0 0 1.25]

    L=
    [1 0 0]
    [.25 1 0]
    [.775 0.5 1]
     
  2. jcsd
  3. Oct 7, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Do your L and U matrices, when multiplied together, give the original matrix of coefficients? The first row of your U is identical to the third row of the coefficient matrix. Coincidence?
     
  4. Oct 8, 2013 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Please show your work details, step-by-step. When I do it (with [-8,-2,5] in row 1 and [3,-2,1] in row 3) I get a different U from yours and do not need any more "partial" pivots; straight pivoting works perfectly well. Or, maybe, I have not understood your question---but I still get a different U.
     
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