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May 4, 2011 at 11:31 comment added Federico Poloni This idea is widely studied in numerical linear algebra; unfortunately, often it does not give computationally sound results after the first few eigenvectors since orthogonality w.r.t. the first $v_i$'s is a property that is easily lost numerically. Better solutions are the orthogonal iteration and in general Krylov subspace methods, which try to compute all the eigenvalues at the same time rather than one after the other.
May 4, 2011 at 11:15 comment added Roland Bacher Sorry for the teX problem which I was unable to solve.
May 4, 2011 at 11:12 history answered Roland Bacher CC BY-SA 3.0