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Scaled Partial Pivoting

  1. Mar 30, 2006 #1
    Hi all,
    I have a problem with the question below:

    Suppose that
    2x_1 + x_2 + 3x_3 = 1
    4x_1 + 6x_2 + 8x_3 = 5
    6x_1 + ax_2 + 10x_3 = 5
    where |a| < 10. For which of the following values of a will there be no row interchange required when solving this system using scaled partial pivoting?
    a = 6, a = 9, a = -3

    The answer in the book says a = 6, but I fail to see how any of the 3 values of a requires row interchange at all.

    Here's my reasoning:
    Largest coefficient in Row 1 = 3
    Largest coefficient in Row 2 = 8
    Largest coefficient in Row 3 = 10

    2/3 = 0.67
    4/8 = 0.5
    6/10 = 0.6

    In all 3 cases, a does not affect the results at all, which is the largest ratio is 0.67, so there is no need for row interchange. Also, I can solve all 3 linear systems without row interchanging at all.

    What am I missing?

    Thank you.

    Regards,
    Rayne
     
  2. jcsd
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