510 theorem let a mn with eigenvalues 1 2 n

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Unformatted text preview: 1 02 01 10 A1 = = = = Q 1 R1 01 10 10 10 02 ￿ ￿￿ ￿￿ ￿ 10 01 01 A2 = = = A0 02 10 20 So from here on, the cycle repeats. This leads to repeated A￿j s which fails to converge. Q: What conditions ensure convergence of the QR algorithm? 2.5.10 Theorem. Let A ∈ Mn with eigenvalues λ1 , λ2 , . . . , λn (multiplicity counted) and |λj | = ￿ |λk | for j ￿= k . Then the QR algorithm converges • The rate at which it converges deals with the relation between |λj | and |λk | Reality Check: What about matrices with real entries? What works and what does not? 2.5...
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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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