Some Extensions of the Crouzeix-Palencia Result
Joint with Trevor Caldwell and Kenan Li. Submitted to SIAM Jour. Matrix Anal. Appl.,
2017.
On the Convergence Rate of DGMRES
Joint with Faranges Kyanfar and Abbas Salemi. Submitted to Lin. Alg. Appl., 2017.
Numerical Investigation of Crouzeix's Conjecture
Joint with Michael Overton. Accepted in Lin. Alg. Appl., 2017.
Variational Analysis of the Crouzeix Ratio
Joint with Adrian Lewis and Michael Overton. Math Programming (2016).
Near Normal Dilations of Nonnormal Matrices
Joint with Trevor Caldwell and Kenan Li. SIAM Jour. Matrix Anal. Appl. 37 (2016),
pp. 1365-1381.
An Algorithm for Finding a 2-Similarity Transformation from a Numerical Contraction
to a Contraction
Joint with Daeshik Choi. SIAM Jour. Matrix Anal. Appl. 36 (2015), pp. 1248-1262.
Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture
Joint with Daeshik Choi. SIAM Jour. Matrix Anal. Appl. 36 (2015), pp. 289-301.
Analysis of an Aggregation-Based Two-Grid Method for a Rotated Anisotropic Diffusion
Problem
Joint with Meng-Huo Chen. Num. Lin. Alg. Appl. 22 (2015), pp. 681-701.
Crouzeix's Conjecture and Perturbed Jordan Blocks
Joint with Daeshik Choi. Lin. Alg. Appl. 436 (2012), pp. 2342-2352.
Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport
Equation
Joint with Britton Chang and Eric Machorro. Num. Lin. Alg. Appl. 18 (2011), pp. 141-154.
Upper and Lower Bounds on Norms of Functions of Matrices
Lin. Alg. Appl. 430 (2009), pp. 52-65.
Fourth Order Accurate Evaluation of Integrals in Potential Theory on Exterior
Regions
Joint with Anita Mayo. Jour. Comput. Phys. 220 (2007), pp. 900-914.
Characterizations of the Polynomial Numerical Hull of Degree k
Joint with James Burke. Lin. Alg. Appl. 419 (2006), pp. 37-47.
Some Theoretical Results Derived from Polynomial Numerical Hulls of Jordan
Blocks
Elec. Trans. Num. Anal. 18 (2004), pp. 81-90.
Card Shuffling and the Polynomial Numerical Hull of Degree k
SIAM J. Sci. Comput. 25 (2004), pp. 408-416.
The Polynomial Numerical Hulls of Jordan Blocks and Related Matrices
Joint with Vance Faber and Don Marshall. Lin. Alg. Appl. 374 (2003), pp. 231-246.
Generalizations of the Field of Values Useful in the Study of Polynomial
Functions of a Matrix
Lin. Alg. Appl. 347 (2002), pp. 233-249.
On Solving Indefinite Linear Systems by Means of the Lanczos Method
Joint with Vladimir Druskin and Leonid Knizhnerman. Jour. Comput. Math. and
Math. Phys. 39 (1999), pp. 350-356.
Rapid Parallel Evaluation of Integrals in Potential Theory
Joint with Anita Mayo. Jour. Comp. Phys. 145 (1998), pp. 731-742.
Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions
Joint with Vladimir Druskin and Leonid Knizhnerman. SIAM Jour. Sci. Comput. 19
(1998), pp. 38-54.
Numerical Behavior of the Modified Gram-Schmidt GMRES Implementation
Joint with Miro Rozloznik and Zdenek Strakos. BIT 37 (1997), pp. 706-719.
Estimating the Attainable Accuracy of Recursively Computed Residual Methods
SIAM J. Matrix Anal. Appl., 18 (1997), pp. 535-551.
Any Nonincreasing Convergence Curve is Possible for GMRES
Joint with Vlastimil Ptak and Zdenek Strakos. SIAM J. Matrix Anal. Appl., 17 (1996),
pp. 465-469.
Relations Between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear
Systems
Joint with Jane Cullum. SIAM J. Matrix Anal. Appl. 17 (1996), pp. 223-247.
Krylov Subspace Approximations to the Solution of a Linear System
in Linear and Nonlinear Conjugate Gradient Methods, L. Adams and J. Nazareth, eds.,
SIAM, 1996.
Numerical Stability of GMRES
Joint with J. Drkosova, Miro Rozloznik, and Zdenek Strakos. BIT 35 (1995), pp. 309-331.
A Further Note on Max-min Properties of Matrix Factor Norms
Joint with Leonid Gurvits. SIAM J. Sci. Comput. 16 (1995), pp. 496-499.
Max-Min Properties of Matrix Factor Norms
Joint with Leonid Gurvits. SIAM J. Sci. Comput. 15 (1994), pp. 348-358.
GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
Joint with Nick Trefethen. SIAM J. Sci. Comput. 15 (1994), pp. 359-368.
The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
in Proceedings of the Cornelius Lanczos International Centenary Conference, J. Brown, M. Chu,
D. Ellison, and R. Plemmons, eds., SIAM, 1994.
Matrices that Generate the Same Krylov Residual Spaces
Joint with Zdenek Strakos. in IMA Volumes in Applied Mathematics,
Vol. 60: Recent Advances in Iterative Methods, G. Golub,
A. Greenbaum, and M. Luskin, eds., 1994.
Laplace's Equation and the Dirichlet-Neumann Map in Multiply-Connected Domains
Joint with Leslie Greengard and Geoffrey McFadden. Jour. Comp. Phys. 105 (1993),
pp. 267-278.
On the Numerical Solution of the Biharmonic Equation in the Plane
Joint with Leslie Greengard and Anita Mayo. Physica D 60 (1992), pp. 216-225.
Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on
Irregular Domains
Joint with Anita Mayo. SIAM J. Sci. Stat. Comput. 13 (1992), pp. 101-118.
Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations
Joint with Zdenek Strakos. SIAM J. Matrix Anal. Appl. 13 (1992), pp. 121-137.
Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential
Operators
SIAM J. Matrix Anal. Appl. 13 (1992), pp. 826-846.
Behavior of Slightly Perturbed Lanczos and Conjugate Gradient Recurrences
Lin. Alg. Appl., 113 (1989), pp. 7-63.
Optimal Preconditioners of a Given Sparsity Pattern
Joint with Garry Rodrigue. BIT 29 (1989), pp. 610-634.
Parallelizing Preconditioned Conjugate Gradient Algorithms
Joint with Congming Li and Han Zheng Chao. Computer Phys. Comm. 53 (1989), pp. 295-309.
Comparison of Linear System Solvers Applied to Diffusion-Type Finite Element
Equations
Joint with Congming Li and Han Zheng Chao. Num. Math. 56 (1989), pp. 529-546.
Synchronization Costs on Multiprocessors
Parallel Computing 10 (1989), pp. 3-14.
Global Boundary Conditions and Fast Helmholtz Solvers
Joint with Bjorn Engquist and William Murphy. IEEE Trans. on Magnetics, 25 (1989),
pp. 2804-2806.
A New Scheme for Multi-Dimensional Line Transfer. I. Formulation
and 1-D Results
Joint with Richard Klein, John Castor, Derek Taylor, and Pieter Dykema.
Journal of Quantitative Spectroscopy and Radiative Transfer 41 (1989), pp. 199-219.
A Multigrid Method for Multiprocessors
Appl. Math. and Comp. (1986), pp. 75-88.
A Petrov-Galerkin Finite Element Method for Solving the Neutron Transport Equation
Joint with James Ferguson. Jour. Comp. Phys., April, 1986.
Analysis of a Multigrid Method as an Iterative Technique for Solving Linear Systems
SIAM J. Num. An., pp. 473--485, June, 1984.
Convergence Properties of the Conjugate Gradient
Algorithm in Exact and Finite Precision Arithmetic
Ph.D. Dissertation, University of California, Berkeley, June, 1981.
Comparison of Splittings Used with the Conjugate Gradient Algorithm
Num. Math., 33 (1979), pp. 181-194.
Approximating the Inverse of a Matrix for Use in Iterative Algorithms on
Vector Processors
Joint with Paul Dubois and Garry Rodrigue. Computing (1979), pp. 257-268.
Lens and Mirror Design Via the Principal Surface
Joint with Alexamder Glass and John Trenholme. Applied Optics, 15 (1976), pp. 2579-2582.