Selected Works of David S. Watkins

1. Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, and David S. Watkins, Core-Chasing Algorithms for the Eigenvalue Problem, SIAM, Philadelphia, 2018, x+149 pp., ISBN: 978-1-611975-33-8.

2. David S. Watkins, Fundamentals of Matrix Computations, Third Edition, John Wiley and Sons, 2010, xvi+644 pp., ISBN: 978-0-470-52833-4.

3. David S. Watkins, The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM, Philadelphia, 2007, x+442 pp., ISBN 978-0-898716-41-2.

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4. David S. Watkins, Understanding the QR algorithm, SIAM Review, 24 (1982), pp. 427-440.
   I list this paper because it's the one that put me on the map.
   My views have changed significantly since then. See the books listed above and this:

5. David S. Watkins, Francis's algorithm, (.pdf) Amer. Math. Monthly, 118 (2011), pp. 387-403.

6. D. S. Watkins and L. Elsner, On Rutishauser's approach to selfsimilar flows, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 301-311.
   (One paper to represent my work on Toda-like flows in the 80s.)

7. D. S. Watkins and L. Elsner, Convergence of algorithms of decomposition type for the eigenvalue problem (.ps), Linear Algebra Appl., 143 (1991), pp. 19-47. This was the basis for a chapter in my 2007 SIAM book.

8. David S. Watkins, Some perspectives on the eigenvalue problem, SIAM Review, 35 (1993), pp. 430-471.

9. David S. Watkins, The transmission of shifts and shift blurring in the QR algorithm (.ps), Linear Algebra Appl., 241-243 (1996), pp. 877-896.

10. David S. Watkins, Bulge exchanges in algorithms of QR type (.ps), SIAM J. Matrix Anal. Appl., 19 (1998), pp. 1074-1096.

11. V. Mehrmann and D. S. Watkins, Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils, (.ps), SIAM J. Sci. Comput., 22 (2001), pp. 1905-1925. epubs.siam.org.

    For an (easier-to-read) update see this:

    David S. Watkins, Large-scale structured eigenvalue problems, Chapter 2 in Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory. A Festschrift in honor of Volker Mehrmann, Springer-Verlag, 2015.

12. David S. Watkins, On Hamiltonian and symplectic Lanczos processes, Linear Algebra Appl., 385 (2004) pp. 23-45,
    but this is done better in my 2007 SIAM book.

13. David S. Watkins, Product eigenvalue problems (.pdf), SIAM Review, 47 (2005), pp. 3-40. epubs.siam.org
    This became a chapter in my 2007 SIAM book.

14. Daniel Kressner, Christian Schroeder, and David S. Watkins, Implicit QR algorithms for palindromic and even eigenvalue problems, Numer. Algorithms, 51 (2009), pp. 209-238. electronic publication

15. Raf Vandebril and David S. Watkins, A generalization of the multishift QR algorithm, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 759-779.

16. Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins, Fast and backward stable computation of roots of polynomials, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 942-973. (.pdf)
    2017 SIAM Outstanding Paper Prize.