David S. Watkins

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All published works

Action	Title	Year	Authors
+ PDF Chat	The RQR algorithm	2024	Daan Camps Thomas Mach Raf Vandebril David S. Watkins
+ PDF Chat	Pole-Swapping Algorithms for Alternating and Palindromic Eigenvalue Problems	2020	Thomas Mach Thijs Steel Raf Vandebril David S. Watkins
+ PDF Chat	On pole-swapping algorithms for the eigenvalue problem	2020	Daan Camps Thomas Mach Raf Vandebril David S. Watkins
+	Pole-swapping algorithms for alternating and palindromic eigenvalue problems	2019	Thomas Mach Thijs Steel Raf Vandebril David S. Watkins
+	On pole-swapping algorithms for the eigenvalue problem	2019	Daan Camps Thomas Mach Raf Vandebril David S. Watkins
+	Pole-swapping algorithms for alternating and palindromic eigenvalue problems	2019	Thomas Mach Thijs Steel Raf Vandebril David S. Watkins
+	Core-Chasing Algorithms for the Eigenvalue Problem	2018	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+ PDF Chat	Fast and Backward Stable Computation of Roots of Polynomials, Part II: Backward Error Analysis; Companion Matrix and Companion Pencil	2018	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials	2017	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials	2016	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Roots of Polynomials: on twisted QR methods for companion matrices and pencils	2016	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Fast and backward stable computation of the eigenvalues of matrix polynomials	2016	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	A note on companion pencils	2016	Jared L. Aurentz Thomas Mach Raf Vandebril David S. Watkins
+	A note on compacnion pencils	2016	Jared L. Aurentz Thomas Mach Raf Vandebril David S. Watkins
+	Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil	2016	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials	2016	Jared L. Aurentz Thomas Mach Leonardo Robol Raf Vandebril David S. Watkins
+	Large-Scale Structured Eigenvalue Problems	2015	David S. Watkins
+	<scp>QR</scp>Algorithm	2014	David S. Watkins
+	Fast and stable computation of the roots of polynomials	2014	Jared L. Aurentz Thomas Mach Raf Vandebril David S. Watkins
+	Roots of polynomials	2014	Raf Vandebril Thomas Mach David S. Watkins Jared L. Aurentz
+ PDF Chat	Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix	2013	Jared L. Aurentz Raf Vandebril David S. Watkins
+	An extension of the QZ algorithm beyond the Hessenberg-upper triangular pencil	2013	Raf Vandebril David S. Watkins
+	Fast computation of zeros of a polynomial	2012	David S. Watkins Raf Vandebril Jared L. Aurentz
+	The effect of electron interactions on the universal properties of systems with optimized intrinsic off-resonant hyperpolarizability	2011	David S. Watkins Mark G. Kuzyk
+	The effect of electron interactions on the universal properties of systems with optimized intrinsic off-resonant hyperpolarizability	2011	David S. Watkins Mark G. Kuzyk
+ PDF Chat	MAXIMIZING THE HYPERPOLARIZABILITY OF ONE-DIMENSIONAL SYSTEMS	2010	Urszula B. Szafruga Mark G. Kuzyk David S. Watkins
+ PDF Chat	Implicit QR algorithms for palindromic and even eigenvalue problems	2008	Daniel Kreßner Christian Schröder David S. Watkins
+ PDF Chat	Optimizing potential energy functions for maximal intrinsic hyperpolarizability	2007	Juefei Zhou Urszula B. Szafruga David S. Watkins Mark G. Kuzyk
+ PDF Chat	6. The Generalized Eigenvalue Problem	2007	David S. Watkins
+ PDF Chat	Pushing the hyperpolarizability to the limit	2006	Juefei Zhou Mark G. Kuzyk David S. Watkins
+ PDF Chat	The effects of geometry on the hyperpolarizability	2006	Mark G. Kuzyk David S. Watkins
+	ON THE REDUCTION OF A HAMILTONIAN MATRIX TO HAMILTONIAN SCHUR FORM	2006	David S. Watkins
+ PDF Chat	Efficient Implementation of the Multishift $QR$ Algorithm for the Unitary Eigenvalue Problem	2006	Roden Jason A. David David S. Watkins
+ PDF Chat	Product Eigenvalue Problems	2005	David S. Watkins
+	On Hamiltonian and symplectic Lanczos processes	2004	David S. Watkins
+	On Hamiltonian and symplectic Lanczos processes	2004	David S. Watkins
+	Numerical Solution of Structured Problems	2004	Thomas Apel Volker Mehrmann David S. Watkins
+	Iterative Methods for Linear Systems	2002	David S. Watkins
+	The Least Squares Problem	2002	David S. Watkins
+ PDF Chat	The Singular Value Decomposition (SVD)	2002	David S. Watkins
+	Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils	2001	Volker Mehrmann David S. Watkins
+	Cholesky-like Factorizations of Skew-Symmetric Matrices	2000	Peter Benner Ralph Byers Heike Faßbender Volker Mehrmann David S. Watkins
+	Performance of the <i>QZ</i> Algorithm in the Presence of Infinite Eigenvalues	2000	David S. Watkins
+	Bulge Exchanges in Algorithms of QR Type	1998	David S. Watkins
+	Two connections between the SR and HR eigenvalue algorithms	1998	Peter Benner Heike Faßbender David S. Watkins
+	Unitary orthogonalization processes	1997	David S. Watkins
+	The transmission of shifts and shift blurring in the QR algorithm	1996	David S. Watkins
+	Forward Stability and Transmission of Shifts in the $QR$ Algorithm	1995	David S. Watkins
+	A class of Hamiltonian-symplectic methods for solving the algebraic Riccati equation	1994	Allen C. Raines David S. Watkins
+ PDF Chat	Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem	1994	David S. Watkins L. Elsner
+	Shifting Strategies for the Parallel $QR$ Algorithm	1994	David S. Watkins
+	Some Perspectives on the Eigenvalue Problem	1993	David S. Watkins
+	A Monotonicity Property for Toda-Type Flows	1991	Percy Deift Saul Rivera Carlos Tomei David S. Watkins
+	Convergence of algorithms of decomposition type for the eigenvalue problem	1991	David S. Watkins L. Elsner
+ PDF Chat	On Rutishauser’s Approach to Self-Similar Flows	1990	David S. Watkins L. Elsner
+	Generic (gr) decomposition algorithms for the nonsymmetric matrix eigenvalue problem	1990	Jeffrey Burgess Haag David S. Watkins
+ PDF Chat	Self-equivalent flows associated with the generalized eigenvalue problem	1989	David S. Watkins L. Elsner
+	Self-Equivalent Flows Associated Decomposition	1989	David S. Watkins L. Elsner
+	Isospectral Flows	1984	David S. Watkins
+	An Initialization Program for Separably Stiff Systems	1983	David S. Watkins
+	Understanding the $QR$ Algorithm	1982	David S. Watkins
+	Efficient Initialization of Stiff Systems with One Unknown Initial Condition	1981	David S. Watkins
+	Determining Initial Values for Stiff Systems of Ordinary Differential Equations	1981	David S. Watkins
+	Comparison of solutions to the thirteen-moment and standard transport equations for low speed thermal proton flows	1979	R. W. Schunk David S. Watkins
+	Error Bounds for Polynomial Blending Function Methods	1977	David S. Watkins
+	Bases of Splines Associated with Constant Coefficient Differential Operators	1975	Eckard Schmidt Peter Lancaster David S. Watkins

Common Coauthors

Coauthor	Papers Together
Raf Vandebril	21
Thomas Mach	15
Jared L. Aurentz	14
Leonardo Robol	8
Mark G. Kuzyk	6
Thijs Steel	3
Volker Mehrmann	3
L. Elsner	3
Daan Camps	3
Thomas Mach	3
Heike Faßbender	2
L. Elsner	2
Peter Benner	2
Urszula B. Szafruga	2
Juefei Zhou	2
Jeffrey Burgess Haag	1
Allen C. Raines	1
Percy Deift	1
Thomas Apel	1
Carlos Tomei	1
Christian Schröder	1
Peter Lancaster	1
Roden Jason A. David	1
Daniel Kreßner	1
Saul Rivera	1
Eckard Schmidt	1
Ralph Byers	1
R. W. Schunk	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	An Algorithm for Generalized Matrix Eigenvalue Problems	1973	C Moler G. W. Stewart	13
+	Convergence of algorithms of decomposition type for the eigenvalue problem	1991	David S. Watkins L. Elsner	12
+ PDF Chat	Vector Spaces of Linearizations for Matrix Polynomials	2006	D. Steven Mackey Niloufer Mackey Christian Mehl Volker Mehrmann	7
+ PDF Chat	Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem	1994	David S. Watkins L. Elsner	6
+	The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution	1991	Volker Mehrmann	6
+ PDF Chat	Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations	2006	D. Steven Mackey Niloufer Mackey Christian Mehl Volker Mehrmann	6
+	Ordinary Differential Equations and the Symmetric Eigenvalue Problem	1983	Percy Deift T. Nanda Carlos Tomei	6
+	On swapping diagonal blocks in real Schur form	1993	Zhaojun Bai James Demmel	6
+	The transmission of shifts and shift blurring in the QR algorithm	1996	David S. Watkins	6
+	Understanding the $QR$ Algorithm	1982	David S. Watkins	6
+	Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils	2001	Volker Mehrmann David S. Watkins	6
+ PDF Chat	Computing eigenspaces with specified eigenvalues of a regular matrix pair (A, B) and condition estimation: theory, algorithms and software	1996	Bo Kågström Peter Poromaa	5
+	Isospectral Flows	1984	David S. Watkins	5
+	An analysis of the HR algorithm for computing the eigenvalues of a matrix	1981	Angelika Bunse‐Gerstner	5
+ PDF Chat	A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix	1984	Charles Van Loan	5
+	An extension of the QZ algorithm beyond the Hessenberg-upper triangular pencil	2013	Raf Vandebril David S. Watkins	5
+ PDF Chat	Der Quotienten-Differenzen-Algorithmus	1954	Heinz Rutishauser	5
+	Schur parameter pencils for the solution of the unitary eigenproblem	1991	Angelika Bunse‐Gerstner L. Elsner	5
+	A symplectic QR like algorithm for the solution of the real algebraic Riccati equation	1986	Angelika Bunse‐Gerstner Volker Mehrmann	5
+	The QR algorithm for unitary Hessenberg matrices	1986	William B. Gragg	5
+	ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION	1989	Zhaojun Bai James Demmel	5
+	The Symmetric Eigenvalue Problem.	1981	J. H. Wilkinson Beresford Ν. Parlett	5
+	Forward Stability and Transmission of Shifts in the $QR$ Algorithm	1995	David S. Watkins	4
+ PDF Chat	Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities	2005	Mark G. Kuzyk	4
+ PDF Chat	Implicit QR algorithms for palindromic and even eigenvalue problems	2008	Daniel Kreßner Christian Schröder David S. Watkins	4
+	A Generalized Eigenvalue Approach for Solving Riccati Equations	1981	Paul Van Dooren	4
+	A Geometric Theory for the $QR$, $LU$ and Power Iterations	1973	Beresford Ν. Parlett William G. Poole	4
+	An iteration method for the solution of the eigenvalue problem of linear differential and integral operators	1950	Cornelius Lanczos	4
+	On the eigenproblem for orthogonal matrices	1986	Gregory Ammar William B. Gragg Lothar Reichel	4
+	Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems	1973	G. W. Stewart	4
+	A Hamiltonian $QR$ Algorithm	1986	Ralph Byers	4
+ PDF Chat	TRUNCATED SUM RULES AND THEIR USE IN CALCULATING FUNDAMENTAL LIMITS OF NONLINEAR SUSCEPTIBILITIES	2006	Mark G. Kuzyk	4
+	The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory	1984	Moody T. Chu	4
+ PDF Chat	Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm	2011	Raf Vandebril	4
+	Hamiltonian and symplectic algorithms for the algebraic riccati equation	1983	Ralph Byers	4
+ PDF Chat	LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs	1996	Bo Kågström Peter Poromaa	4
+	A note on companion pencils	2016	Jared L. Aurentz Thomas Mach Raf Vandebril David S. Watkins	4
+ PDF Chat	Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix	2013	Jared L. Aurentz Raf Vandebril David S. Watkins	3
+ PDF Chat	Strongly stable gyroscopic systems	1999	Peter Lancaster	3
+ PDF Chat	A User’s View of Solving Stiff Ordinary Differential Equations	1979	L. F. Shampine C. W. Gear	3
+	Backward error and condition of polynomial eigenvalue problems	2000	Françoise Tisseur	3
+	Comparison of solutions to the thirteen-moment and standard transport equations for low speed thermal proton flows	1979	R. W. Schunk David S. Watkins	3
+	On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems	1977	G. W. Stewart	3
+	Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions	1998	Jeffrey C. Lagarias James A. Reeds Margaret H. Wright Paul E. Wright	3
+ PDF Chat	Self-equivalent flows associated with the generalized eigenvalue problem	1989	David S. Watkins L. Elsner	3
+	Shifting Strategies for the Parallel $QR$ Algorithm	1994	David S. Watkins	3
+	A Schur decomposition for Hamiltonian matrices	1981	Chris Paige Charles Van Loan	3
+	On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$	1972	G. W. Stewart	3
+	Ein infinitesimales Analogon zum Quotienten-Differenzen-Algorithmus	1954	Heinz Rutishauser	3
+	The Symmetric Eigenvalue Problem	1998	Beresford Ν. Parlett	3