6.7 References and Further Reading
The balanced-QR method and its error analysis are 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.
The formulas for divided differences are given in the following texts,
- Abramowitz and Stegun, Handbook of Mathematical Functions,
Sections 25.1.4 and 25.2.26.
- R. L. Burden and J. D. Faires, Numerical Analysis, 9th edition,
ISBN 0-538-73351-9, 2011.