3 thus if an were to converge in the sense of entry

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Unformatted text preview: o A Proof. By definition, An+1 = Rn Qn = Q∗ An Qn since An = Qn Rn implies that Rn = Q∗ An . n n So An+1 and An are unitarily equivalent. Thus, by induction An and A0 are as well. 3 Thus, if An were to converge (in the sense of entry-wise convergence) to an upper triangular matrix, then by unitary equivalence we would know all eigenvalues of A. Problem: QR algorithm may not converge. For example, ￿ ￿￿ ￿￿ ￿ 01 01 20 A0 = = = Q 0 R0 20 10 01 ￿ ￿￿ ￿￿ ￿￿ ￿￿ ￿ 20 0...
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This note was uploaded on 01/16/2014 for the course MATH 6304 taught by Professor Bernhardbodmann during the Fall '12 term at University of Houston.

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