A bibliography on roots of polynomials

John Michael McNamee

In this work we present a comprehensive bibliography on roots of polynomials, covering (hopefully) most published work between the ``Dawn of History'' and 1994. This could be of help to anyone contemplating research into methods of calculating polynomial roots. To keep the length manageable we have excluded theses, unpublished reports, and works in very obscure journals or very obscure languages.

Introduction by J.M. McNamee (excerpt from the 1993 edition)

Addendum to the 1996 hypertext edition

A 2002 update of the supplementary bibliography on roots of polynomials

The general subject of polynomial root finding has been divided into 29 categories that you can search or view:

1. Bracketing methods (real roots only).
2. Newton's method.
3. Simultaneous root-finding methods.
4. Graeffe's method.
5. Integral methods, esp. Lehmer's.
6. Bernoulli's and QD method.
7. Interpolation methods such as secant, Muller's.
8. Minimization methods.
9. Jenkins--Traub method.
10. Sturm sequences, greatest common divisors, resultants.
11. Stability questions (Routh--Hurwitz criterion, etc.).
12. Interval methods.
13. Miscellaneous.
14. Lin and Bairstow methods.
15. Methods involving derivatives higher than first.
16. Complexity, convergence and efficiency questions.
17. Evaluation of polynomials and derivatives.
18. A priori bounds.
19. Low-order polynomials (special methods).
20. Integer and rational arithmetic.
21. Special cases such as Bessel polynomials.
22. Vincent's method.
23. Mechanical devices.
24. Acceleration techniques.
25. Existence questions.
26. Error estimates, deflation, sensitivity, continuity.
27. Roots of random polynomials.
28. Relation between roots of a polynomial and those of its derivative
29. Nth roots.