PAPERS

A general matrix eigenvalue algorithm, SIAM J. Numer. Anal. 12, 1975, 819-834.  (PDF)

Generalizing the singular value decomposition, SIAM J. Numer. Anal. 13, 1976, 76-83. (PDF)

A Study of the Matrix Exponential, Numerical Analysis Report  No. 10, Department of Mathematics, University of Manchester, 1975. (PDF)

The sensitivity of the matrix exponential, SIAM J. Numer. Anal. 14, 1977, 971-981.  (PDF)

The limitations of Pade approximation for computing the matrix exponential . In Pade Approximation, E.B. Saff and R.S. Varga (eds), New York, Academic Press, 1977. (PDF)

Computing integrals involving the matrix exponential, IEEE Transactions on Automatic Control AC-23, 1978, 395-404. (PDF)

Nineteen dubious methods for computing the matrix exponential, SIAM Review 20, 1978, 801-836. (With C.B. Moler.)  (PDF)

A generalized horner algorithm for the computation of integrals involving the matrix exponential. In  Proceedings of the 1978 IEEE Conference on Decision and Control, 74-79. (PDF)

A note on the evaluation of matrix polynomials,  IEEE Transactions on Automatic Control AC-24, 1979, 320-321. (PDF)

Unsymmetric positive definite linear systems, Linear Algebra and It's Applications 28, 1979, 85-97. (With G.H. Golub.)  (PDF)

A Hessenberg-Schur algorithm for AX + XB = C, IEEE Transactions on Automatic Control AC-24, 1979, 909-913. (With G.H. Golub and S. Nash.)  (PDF)

Total Least Squares. In Smoothing Techniques for Curve Estimation, Th. Gasser and M. Rosenblatt (eds), Lecture Notes in Mathematics No. 757, Springer Verlag, New York, 1979. (With G.H. Golub)  (PDF)

An analysis of the total least squares problem, SIAM Journal on Numerical Analysis 17, 1980, 883-893. (With G.H. Golub.)  (PDF)

A Schur decomposition for Hamiltonian matrices, Linear Algebra and It's Applications 41, 1981, 11-32. (With C. Paige.)  (PDF)

Using the Hessenberg Decomposition in Control Theory. In Algorithms and Theory in Filtering and Control, D.C. Sorensen and R.J.-B. Wets (eds), Mathematical Programming Study No. 18, North-Holland, Amsterdam, 1982. (PDF)

Generalizing the Linpack Condition Estimator. In Numerical Analysis, J.P. Hennart (ed), Lecture Notes in Mathematics No. 909, Springer-Verlag, New York, 1982. (with A.K. Cline and A.R. Conn). (PDF)

A Generalized SVD Analysis of Some Weighting Methods for Equality Constrained Least Squares. In  Matrix Pencils Proceedings, Pite Havsbad, 1982, B. Kagstrom and A. Ruhe (eds), Lecture Notes in Mathematics No. 973, Springer-Verlag, New York, 1983. (PDF)

Computation of the Generalized Singular Value Decomposition Using Mesh Connected Processors,  Proceedings of the SPIE, 1983. (With R. Brent and F. Luk). (PDF)

A symplectic method for computing all the eigenvalues of a Hamiltonian matrix, J. Linear Algebra and Its Applications, 61, 1984, 233-251. (PDF)

Signal Processing Computations Using the Generalized Singular Value Decomposition, Proceedings SPIE, Vol. 495, SPIE International Symposium, San Diego, August, 1984. (with J. Speiser). (PDF)

Computation of the Singular Value Decomposition Using Mesh-Connected Processors, J. of VLSI and Computer Systems 1, 1985, 242-270 (With R. Brent and F. Luk).  (PDF)

On the Method of Weighting for Equality Constrained Least Squares Problems, SIAM J. Numer. Analysis, 22, 1985, 851-864. (PDF)

Computing the CS and the Generalized Singular Value Decompositions, Numerische Mathematik, 46, 1985, 479-491. (PDF)

How Close is a Matrix to Being Unstable? In  Contemporary Mathematics Vol. 47, Linear Algebra and Systems Theory, American Mathematical Society, (pp.465-478), 1985. (PDF)

Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix, SIAM J. Scientific and Statistical Computing, 1986, 123-131. (With G. Cybenko.) (PDF)

Parallel Algorithms for Constrained and Unconstrained Least Squares problems, in Numerical Analysis, D.F.Griffiths and G.A.Watson (eds), Pitman Research Notes, Longman Scientific and Technical, Harlow, Essex, UK, pp. 112-124, 1986. (PDF)

The Block Jacobi Method for Computing the Singular Value decomposition, in Computational and combinatorial methods in systems theory, C. Byrnes and A. Lindquist (eds), North-Holland, pp. 245-256, 1986. (PDF)

Computing the Singular Value Decomposition on a Ring of Array Processors, in Large scale eigenvalue problems, J. Cullum and R. Willoughby (eds), Elsevier, pp.51-66, 1986, (with C. Bischof.)  (PDF)

Computation of the CS decomposition with applications to signal processing . In SPIE Proceedings, Vol. 696, 1986. (with J. Speiser) (PDF)

The WY Representation for Products of Householder Transformations, SIAM J. Scientific and Statistical Computing, 8, 1987, s2-s13. (With C. Bischof.)  (PDF)

On Estimating the Condition of Eigenvalues and Eigenvectors, Linear Algebra and Its Applications, 88, 1987, 715-732. (PDF)

A Unitary Method for the ESPRIT Direction-of-Arrival Estimation Algorithm, Proceedings of the SPIE, 1987. (PDF)

A Block QR Factorization Scheme for Loosely Coupled Systems of Array Processors, in Algorithms for Modern Parallel Computer Architectures, Springer-Verlag, Martin Schultz (ed), 1988, 217-228. (PDF)

Matrix Computations and Signal Processing, Proceedings of the McMaster Symposium on Signal Processing, Prentice-Hall, 1988. (PDF)

The Strong Stability of Algorithms for Solving Symmetric Linear Systems, SIAM Journal on Matrix Analysis and Applications, 10, 1989, 494-99 (with J . Bunch and J. Demmel). (PDF)

A Storage Efficient WY Representation for Products of Householder Transfor mations, SIAM Journal on Scientific and Statistical Computing, 10, 1989, 53-57 (wit h R. Schreiber). (PDF)

High Performance GEMM-Based Level-3 BLAS: Sample Routines for Double Precision Real Data, in High Performance Computing II, M. Durand and F. Dabaghi (eds), North Holland, 1991 (with B. Kagstrom and P. Ling). (PDF)

Parallel Block Algorithms on the Shared Memory Multiprocessor  IBM 3090 VF/600J,   International Journal on Supercomputing Applications, 1992, 6, 69-97(with B. Kagstrom, E. Elmroth, and K. Dackland). (PDF)

A Survey of Matrix Computations, in Handbooks in Operations Research and Management Science, Volume 3: Computing, E.G. Coffman, J.K. Lenstra, and A.H.G. Rinnooy Kan (Eds), 1992, North Holland, 247-322. (PDF)

Approximation with Kronecker Products, in Linear Algebra for Large Scale and Real-Time Applications, M.S. Moonen and G.H. Golub (eds), Kluwer Publications, 1993, 293-314 (with N. Pitsianis). (PDF)

Optimizing closed-loop Adaptive-Optics Performance with Use of Multiple Control Bandwidths, Journal of the Optical Society of America A, 1994, 2871-2886 (with B.L. Ellerbroek, N.P. Pitsianis, and R.J. Plemmons) (PDF)

GEMM-Based Level 3 BLAS: Algorithms for the Model Implementations,  ACM Transactions on Mathematical Software 24 (1999), 268-302. (with P. Ling and B. Kagstrom) (PDF)

Algorithm 784. GEMM-Based  Level 3 BLAS: Portability and Optimization Issues,  ACM Transactions on Mathematical Software 24 (1999), 303-316. (with P. Ling and B. Kagstrom) (PDF)

Rational Matrix Functions and Rank-One Updates, SIAM J. Matrix Analysis and Applications, 22(2000), 145-154. (with D.S. Bernstein). (PDF)

The Ubiquitous Kronecker Product, Journal of Computational and Applied Mathematics, 123(2000), 85-100. (PDF)

Product Triangular Systems with Shift, SIAM J. Matrix Analysis and Applications, 24(2002), 292-301. (with Carla Dee Martin). (PDF)

Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, SIAM Review 45(2003), 3--49. (with Cleve Moler). (PDF)

Solving Real Linear Systems with the Complex Schur Decomposition,  SIAM J. Matrix Analysis and Applications, 29(2007), 177-183. (with Carla D. Martin). (PDF)

Shifted Kronecker Product Systems, SIAM J. Matrix Analysis and Applications, 29(2007), 184-98. (with Carla Dee Martin). (PDF)

A Jacobi-Type Method for Computing orthogonal Tensor Decompositions, SIAM J. Matrix Analysis and Applications, 30 (2008), 1219-1232. ( with Carla D. Martin) (PDF).

From Random Polygon to Ellipse, SIAM Review, 52 (2010), 151-170. (with Adam Elmachtoub). (PDF)

A Higher Order Generalized Singular Value Decompoistion for Comparison of Global mRNA Expression from Multiple Organisims, PLoS One, 6 (2011) Issue 12. (With Sri Priya Ponnapalli, M.A. Saunders, and Orly Alter) (PDF)

Block Tensor Unfoldings, SIAM J. Matrix Analysis and Applications, 33(2012), 149169. (with Stefan Ragnarsson) (PDF)

Block tensors and Symmetric Embeddings, Linear Algebra and its Applications. 438 (2012), 853-874. (with Stefan Ragnarsson) (PDF)