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QR Algorithm 3x3 Matrix

  • 08-11-2013 3:01pm
    #1
    Iancar29
    Registered Users, Registered Users 2 Posts: 5,068 ✭✭✭


    Hi Guys , just looking for some help explaining the QR algorithm for a 3x3 matrix .

    Heres the example im doing ,

    Find the eigen values of A & preform 2 iterations of the QR algorithm to approximate them .


    A = 1 0 0
    0 6 -2
    0 -2 4

    So heres the following that i know.

    ( A- λI ) = 1-λ 0 0
    0 6-λ -2
    0 -2 4-λ

    det(A - λI ) = 1-λ 0 0 1-λ 0
    0 6-λ -2 0 6-λ
    0 -2 4-λ 0 -2


    = (1-λ )(6-λ )(4-λ ) - ( 4-λ )

    = then i get λ1 = 4 , λ 2 = 1 and λ 3 = 6


    SO then i need to Get A into its factors ( Q and R ) , then get the product of RQ.

    But i dunno how to do this step as it seemed very rushed in class.

    Any help much appreciated :)


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