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The Rayleigh quotient iteration

  1. Oct 3, 2009 #1
    I am trying to apply the Rayleigh quotient iteration to the matrix A=

    a 0
    0 b

    where a is different from b (a and b are reals).

    Find the subsets S of R^2(Reals^2) having the property that the iteration applied to this matrix with initial guesses in S do not converge. Is S a set of measure 0?

    I know the Rayleigh quotient is R(A,x)=x*Ax/x*x for A Hermitian and x nonzero. I am supposed to begin with an eigenvalue guess mo and an eigenvector guess vo and use the R.Q. but I am not sure which guesses should I begin with.

    I am not sure how to proceed here. Any help is much appreciated.
     
  2. jcsd
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