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The balanced-QR method and its error analysis is described in the
following papers.
-
R.S. Martin, G. Peters and J.H. Wilkinson, "The QR Algorithm for Real
Hessenberg Matrices", Numerische Mathematik, 14 (1970), 219--231.
-
B.N. Parlett and C. Reinsch, "Balancing a Matrix for Calculation of
Eigenvalues and Eigenvectors", Numerische Mathematik, 13 (1969),
293--304.
-
A. Edelman and H. Murakami, "Polynomial roots from companion matrix
eigenvalues", Mathematics of Computation, Vol. 64 No. 210
(1995), 763--776.
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