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02
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A1 =
=
=
= Q 1 R1
01
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10
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A2 =
=
= A0
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So from here on, the cycle repeats. This leads to repeated Aj 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.
 Fall '12
 BernhardBodmann
 Math, Matrices

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