Mathematics and StatisticsDavid Watkins

David Watkins

  1. Emeritus
Email Addresswatkins@wsu.edu

Biography

Google Scholar

Selected Works

  • 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.
  • David S. Watkins, Fundamentals of Matrix Computations, Third Edition, John Wiley and Sons, 2010, xvi+644 pp., ISBN: 978-0-470-52833-4.
  • David S. Watkins, The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM, Philadelphia, 2007, x+442 pp., ISBN 978-0-898716-41-2.
  • 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:
  • David S. Watkins, Francis’s algorithm, Amer. Math. Monthly, 118 (2011), pp. 387-403.
  • 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.)
  • D. S. Watkins and L. Elsner, Convergence of algorithms of decomposition type for the eigenvalue problem, Linear Algebra Appl., 143 (1991), pp. 19-47. This was the basis for a chapter in my 2007 SIAM book.
  • David S. Watkins, Some perspectives on the eigenvalue problem, SIAM Review, 35 (1993), pp. 430-471.
  • David S. Watkins, The transmission of shifts and shift blurring in the QR algorithm, Linear Algebra Appl., 241-243 (1996), pp. 877-896.
  • David S. Watkins, Bulge exchanges in algorithms of QR type, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 1074-1096.
  • V. Mehrmann and D. S. Watkins, Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils, SIAM J. Sci. Comput., 22 (2001), pp. 1905-1925. 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.
  • 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.
  • David S. Watkins, Product eigenvalue problems, SIAM Review, 47 (2005), pp. 3-40. (epubs.siam.org) This became a chapter in my 2007 SIAM book.
  • 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
  • Raf Vandebril and David S. Watkins, A generalization of the multishift QR algorithm, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 759-779.
  • 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.
    2017 SIAM Outstanding Paper Prize.

Books

  • Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, and David S. Watkins
    Core-Chasing Algorithms for the Eigenvalue Problem SIAM, Philadelphia, July 2018, x+149 pp.
    ISBN 978-1-611975-33-8
  • The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
    SIAM, Philadelphia, November 2007, x+442 pp.
    ISBN 978-0-898716-41-2A modest collection of MATLAB codes to accompany the book. Errata. Read a review of this book by Daniel Szyld in Math. Comp. 78 (2009), pp. 2445–2446.

    Read a review by Beresford Parlett in SIAM Review 52 (2010), pp. 771-774.

  • Fundamentals of Matrix Computations, Third Edition
    John Wiley and Sons, July 2010, xvi+644 pp.
    ISBN: 978-0-470-52833-4
  • Fundamentals of Matrix Computations, Second Edition
    John Wiley and Sons, May 2002, xiv+618 pp.
    ISBN 0-471-21394-2
  • Fundamentals of Matrix Computations, First Edition
    John Wiley and Sons, 1991, xiii+449 pp.
    ISBN 0-471-61414-9

Refereed Publications

  • E. Schmidt, P. Lancaster and D. S. Watkins, Bases of splines associated with constant coefficient differential operators, SIAM J. Numer. Analysis, 12 (1975), pp. 630-645.
  • David S. Watkins, On the construction of conforming rectangular plate elements, Int. J. Num. Meth. Engng., 10 (1976), pp. 925-933.
  • P. Lancaster and D. S. Watkins, Some families of finite elements, J. Inst. Maths. Applics., 19 (1977), pp. 385-397.
  • David S. Watkins, Error bounds for polynomial blending function methods, SIAM J. Numer. Analysis, 14 (1977), pp. 721-734.
  • David S. Watkins, A generalization of the Bramble-Hilbert lemma and applications to multivariate interpolation, J. Approx. Theory, 26 (1979), pp. 219-231.
  • R. W. Schunk and D. S. Watkins, Comparison of solutions to the thirteen-moment and standard transport equations for low-speed thermal proton flows, Planet. Space Sci., 27 (1979), pp. 433-444.
  • David S. Watkins, Determining initial values for stiff systems of ordinary differential equations, SIAM J. Numer. Analysis, 18 (1981), pp. 13-20.
  • David S. Watkins, Efficient initialization of stiff systems with one unknown initial condition, SIAM J. Numer. Anal., 18 (1981), pp. 794-800.
  • R. W. Schunk and D. S. Watkins, Electron temperature anisotropy in the polar wind, J. Geophys. Res., 86 (1981), pp. 91-102.
  • R. W. Schunk and D. S. Watkins, Proton temperature anisotropy in the polar wind, J. Geophys. Res., 87 (1982), pp. 171-180.
  • David S. Watkins, Understanding the QR algorithm, SIAM Review, 24 (1982), pp. 427-440.
  • David S. Watkins, An initialization program for separably stiff systems, SIAM J. Sci. Stat. Comput., 4 (1983), pp. 188-196.
  • D. S. Watkins and R. W. HansonSmith, The numerical solution of separably stiff systems by precise partitioning, ACM Trans. Math. Software, 9 (1983), pp. 293-301.
  • David S. Watkins, Isospectral flows, SIAM Review, 26 (1984), pp. 379-391.
  • D. S. Watkins and L. Elsner, Self-similar flows, Linear Algebra Appl., 110 (1988), pp. 213-242.
  • D. S. Watkins and L. Elsner, Self-equivalent flows associated with the singular value decomposition, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 244-258.
  • D. S. Watkins and L. Elsner, Self-equivalent flows associated with the generalized eigenvalue problem, Linear Algebra Appl., 118 (1989), pp. 107-127.
  • A. Bunse-Gerstner, V. Mehrmann, and D. S. Watkins, An SR algorithm for Hamiltonian matrices based on Gaussian elimination, Meth. Operations Res., 58 (1989), pp. 339-358.
  • D. S. Watkins and L. Elsner, On Rutishauser’s approach to selfsimilar flows, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 301-311.
  • D. S. Watkins and L. Elsner, Convergence of algorithms of decomposition type for the eigenvalue problem, Linear Algebra Appl., 143 (1991), pp. 19-47.
  • D. S. Watkins and L. Elsner, Chasing algorithms for the eigenvalue problem, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 374-384.
  • P. Deift, S. Rivera, C. Tomei, and D. S. Watkins, A monotonicity property for Toda-type flows, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 463-468.
  • David S. Watkins, Bi-directional chasing algorithms for the eigenvalue problem, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 166-179.
  • J. B. Haag and D. S. Watkins, QR-like algorithms for the nonsymmetric eigenvalue problem, ACM Trans. Math. Software, 19 (1993), pp. 407-418.
  • David S. Watkins, Some perspectives on the eigenvalue problem, SIAM Review, 35 (1993), pp. 430-471.
  • D. S. Watkins and L. Elsner, Theory of decomposition and bulge-chasing algorithms for the generalized eigenvalue problem, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 943-967.
  • A. C. Raines III and D. S. Watkins, A class of Hamiltonian-Symplectic methods for solving the algebraic Riccati equation, Linear Algebra Appl., 205/206 (1994), pp. 1045-1060.
  • David S. Watkins, Shifting strategies for the parallel QR algorithm, SIAM J. Sci. Comput., 15 (1994), pp. 953-958.
  • David S. Watkins, Forward stability and transmission of shifts in the QR algorithm, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 469-487.
  • David S. Watkins, The transmission of shifts and shift blurring in the QR algorithm, Linear Algebra Appl., 241-243 (1996), pp. 877-896.
  • David S. Watkins, QR-like algorithms–an overview of convergence theory and practice, pp. 879-893 in Lectures in Applied Mathematics, v. 32, The Mathematics of Numerical Analysis, Ed. J. Renegar, M. Shub, and S. Smale, American Mathematical Society, 1996.
  • David S. Watkins, Unitary orthogonalization processes, J. Comp. Appl. Math., 86 (1997), pp. 335-345.
  • P. Benner, H. Fassbender, and D. S. Watkins, Two connections between the SR and HR eigenvalue algorithms, Linear Algebra Appl., 272 (1998), pp. 17-32.
  • David S. Watkins, Bulge exchanges in algorithms of QR type, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 1074-1096.
  • P. Benner, H. Fassbender, and D. S. Watkins, SR and SZ algorithms for the symplectic (butterfly) eigenproblem</em, Linear Algebra Appl., 287 (1999), pp. 41-76.
  • G. A. Geist, G. W. Howell, and D. S. Watkins, The BR eigenvalue algorithm, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 1083-1098.
  • David S. Watkins, QR-like algorithms for eigenvalue problems, J. Comp. Appl. Math., 123 (2000), pp. 67-83.
  • David S. Watkins, Performance of the QZ algorithm in the presence of infinite eigenvalues, SIAM J. Matrix Anal. Appl., 22 (2000), pp. 364-375.
  • P. Benner, R. Byers, H. Fassbender, V. Mehrmann, and D. S. Watkins, Cholesky-like factorizations of skew-symmetric matrices, Electron. Trans. Numer. Anal., 11 (2000), pp. 85-93.
  • V. Mehrmann and D. S. Watkins, Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils,, SIAM J. Sci. Comput., 22 (2001), pp. 1905-1925.
  • V. Mehrmann and D. S. Watkins, Polynomial eigenvalue problems with Hamiltonian structure, Electron. Trans. Numer. Anal., 13 (2002), pp. 106-118. ETNA website
  • Thomas Apel, Volker Mehrmann, and David S. Watkins, Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elastic structures , Comput. Methods Appl. Mech. Engrg, 191 (2002) pp. 4459-4473. Also available as Preprint, Technische Universitaet Chemnitz, October 2001.
  • G. Henry, D. S. Watkins, and J. J. Dongarra, A parallel implementation of the nonsymmetric QR algorithm for distributed memory architectures, SIAM J. Sci. Comput., 24 (2003) pp. 284-311. epubs.siam.org , also LAPACK Working Note 121 and CRPC-TR97716 .
  • David S. Watkins, On Hamiltonian and symplectic Lanczos processes (.ps), Linear Algebra Appl., 385 (2004) pp. 23-45.
  • Mark Schumaker and David S. Watkins, A framework model based on the Smoluchowski equation in two reaction coordinates, J. Chemical Physics, 121 (2004), pp. 6134-6144.
  • Thomas Apel, Volker Mehrmann, and David S. Watkins, Numerical solution of large-scale structured polynomial or rational eigenvalue problems (.ps), in Foundations of Computational Mathematics, Minneapolis 2002, London Mathematical Society, Lecture Note Series 312. Ed. Felipe Cucker, Ron DeVore, Peter Olver, Endre Suli, Cambridge University Press, (2004) pp. 137-157.
  • David S. Watkins, Product eigenvalue problems (.pdf), SIAM Review, 47 (2005), pp. 3-40. epubs.siam.org
  • David S. Watkins, A case where balancing is harmful (.pdf), Electron. Trans. Numer. Anal., 23 (2006), pp. 1-4. ETNA website
  • Mark G. Kuzyk and David S. Watkins, The effects of geometry on the hyperpolarizability, J. Chemical Physics, 124 (2006), 244104(1-9). (arXiv:physics/0601172),
  • David S. Watkins, On the reduction of a Hamiltonian matrix to Hamiltonian Schur form (.pdf), Electron. Trans. Numer. Anal., 23 (2006), pp. 141-157. ETNA website
  • Roden J. A. David and David S. Watkins, Efficient implementation of the multi-shift QR algorithm for the unitary eigenvalue problem (.pdf), SIAM J. Matrix Anal. Appl., 28 (2006), pp. 623-633
  • Juefei Zhou, Mark G. Kuzyk and David S. Watkins, Pushing the hyperpolarizability to the limit, Optics Letters, 31 (2006), pp. 2891-2893.
  • Juefei Zhou, Mark G. Kuzyk, and David S. Watkins, Reply to “Comment on pushing the hyperpolarizability to the limit”, Optics Letters, 32 (2007), pp. 944-945.
  • Juefei Zhou, Urszula B. Szafruga, David S. Watkins, and Mark G. Kuzyk, Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability, Physical Reviews A, 76 (2007), 053831 pp. 1-10
  • David S. Watkins, The QR algorithm revisited (.pdf), SIAM Review, 50 (2008), pp. 133-145.
  • Roden J. A. David and David S. Watkins, An inexact Krylov-Schur algorithm for the unitary eigenvalue problem (.pdf), Linear Algebra Appl., 429 (2008), pp. 1213-1228.
  • Daniel Kressner, Christian Schroeder, and David S. Watkins, Implicit QR algorithms for palindromic and even eigenvalue problems, TU Berlin, Matheon preprint #432, Numer. Algorithms, 51 (2009), pp. 209-238. electronic publication
  • Volker Mehrmann, Christian Schroeder, and David S. Watkins, A new block method for computing the Hamiltonian Schur form, (.pdf) Linear Algebra Appl., 431 (2009), pp 350-368. link to matrices used as examples in this paper
  • David S. Watkins and Mark G. Kuzyk, Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement J. Chem Phys., 131 (2009), 064110 (8 pages).
  • Urszula B. Szafruga, Mark G. Kuzyk, and David S. Watkins, Maximizing the hyperpolarizability of one-dimensional systems, (.pdf) J. Nonlinear Opt. Phys. Mater., 19 (2010), pp. 379-388.
  • David S. Watkins, Francis’s algorithm, (.pdf) Amer. Math. Monthly, 118 (2011), pp. 387-403.
  • David S. Watkins and Mark G. Kuzyk, The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability, (arXiv:1101.3043 ), J. Chem. Phys., 134, 094109 (2011); doi:10.1063/1.3560031 (10 pages).
  • A. Salam and D. S. Watkins, Structured QR algorithms for Hamiltonian symmetric matrices, Electron. J. Linear Algebra, 22 (2011), pp. 573-585.
  • David S. Watkins and Mark G. Kuzyk, Universal properties of the optimized off-resonant intrinsic second hyperpolarizability, J. Opt. Soc. Am. B, 29 (2012), pp. 1661-1671.
  • Raf Vandebril and David S. Watkins, A generalization of the multishift QR algorithm, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 759-779.
  • Raf Vandebril and David S. Watkins, An extension of the QZ algorithm beyond the Hessenberg-triangular pencil, (.pdf) Electron. Trans. Numer. Anal., 40 (2013), pp. 17-35.
  • Jared L. Aurentz, Raf Vandebril, and David S. Watkins, Fast computation of the zeros of a polynomial via factorization of the companion matrix, (.pdf) SIAM J. Sci. Comput., 35 (2013), pp. A255-A269.
  • Jared L. Aurentz, Raf Vandebril, and David S. Watkins, Fast computation of eigenvalues of companion, comrade, and related matrices, (.pdf) BIT Numer. Math., 54 (2014), pp. 7-30.
  • 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.
  • Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins, Fast and stable unitary QR algorithm, (.pdf) Electron. Trans. Numer. Anal., 44 (2015), pp. 327-341.
  • 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
  • Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins, A note on companion pencils, Contemp. Math., 658 (2016), pp. 91-101. (.pdf)
  • Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins, Computing the eigenvalues of symmetric tridiagonal matrices via a Cayley transform, Electron. Trans. Numer. Anal., 46 (2017), pp. 447-459.
  • Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, and David S. Watkins, Fast and backward stable computation of roots of polynomials, part II: backward error analysis; companion matrix and companion pencil, SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1245-1269. (.pdf)
  • Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, and David S. Watkins, Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials, Math. Comp., 88 (2019), pp. 313-347. (.pdf)
  • Daan Camps, Thomas Mach, Raf Vandebril, and David S. Watkins, On pole-swapping algorithms for the eigenvalue problem, arXiv:1906.08672v3, Electron. Trans. Numer. Anal., 52 (2020), pp. 480-508.
  • Thomas Mach, Thijs Steel, Raf Vandebril, and David S. Watkins, Pole-swapping algorithms for alternating and palindromic eigenvalue problems, arXiv:1906.09942v2, Vietnam J. Math., 48 (2020), pp. 679-701. https://doi.org/10.1007.