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 Abramowitz and Stegun,

• Abramowitz and Stegun, Handbook of Mathematical Functions, Sections 25.1.4 and 25.2.26.