G.W. "Pete" Stewart

Distinguished University Professor Emeritus

2162 Iribe Center

(301) 405-2681

Academic Web Page

Education:

Ph.D., University of Tennessee

Special Awards/Honors:

National Academy of Engineering Member, SIAM Fellow

Biography:

G.W. "Pete" Stewart is a Distinguished University Professor Emeritus of computer science.

Stewart is a world-renowned expert in computational linear algebra. He has made fundamental and highly cited advances in the analysis of rounding error in numerical computations, perturbation of eigensystems, generalized inverses, least squares problems, and matrix factorizations. He has developed efficient algorithms for the singular value decomposition, updating and downdating matrix factorizations, and the eigenproblem that are widely used in applications.

Stewart has published six textbooks, which are models of exposition that have educated multiple generations of researchers. His contributions have led to numerous honors, including election to the National Academy of Engineering and being named a SIAM Fellow.

Stewart received his doctorate from the University of Tennessee in 1968.

Go here to view Stewart‘s academic publications.

Publications

2011

Stewart G.W. 2011. On the Numerical Analysis of Oblique Projectors. SIAM Journal on Matrix Analysis and Applications. 32(1):309-348.

2009

Stewart G.W. 2009. An Unreliable Convergence Criterion for Arnoldi’s Method.

Stewart G.W. 2009. On the Semidefinite B-Arnoldi Method. SIAM Journal on Matrix Analysis and Applications. 31(3):1458-1468.

2008

Stewart G.W. 2008. Block Gram–Schmidt Orthogonalization. SIAM Journal on Scientific Computing. 31(1):761-775.

Lee C-R, Stewart G.W. 2008. Algorithm 879: EIGENTEST—a test matrix generator for large-scale eigenproblems. ACM Trans. Math. Softw.. 35(1):7:1–7:11-7:1–7:11.

2007

Lee C-R, Stewart G.W. 2007. Analysis of the Residual Arnoldi Method. UMIACS-TR-2007-45

Stewart G.W. 2007. A Residual Inverse Power Method. UMIACS-TR-2007-09

2006

Stewart G.W. 2006. The Gram-Schmidt Algorithm and Its Variations. UMIACS-TR-2004-84

Stewart G.W. 2006. A note on generalized and hypergeneralized projectors. Linear Algebra and its Applications. 412(2–3):408-411.

Lee C R, Stewart G.W. 2006. EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems. UMIACS-TR-2006-07

2005

Stewart G.W. 2005. Error Analysis of the Quasi-Gram–Schmidt Algorithm. SIAM Journal on Matrix Analysis and Applications. 27(2):493-506.

Berry MW, Pulatova SA, Stewart G.W. 2005. Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices. ACM Transactions on Mathematical Software-TOMS. 31(2):252-269.

2004

Stewart G.W. 2004. Error Analysis of the Quasi-Gram--Schmidt Algorithm. UMIACS-TR-2004-17

Stewart G.W. 2004. An Elsner-like perturbation theorem for generalized eigenvalues. Linear Algebra and its Applications. 390:1-5.

2003

Stewart G.W. 2003. A Fortran 95 Matrix Wrapper. UMIACS-TR-2003-89

Stewart G.W, Author, Mahajan A, Reviewer. 2003. Matrix Algorithms, Volume II: Eigensystems. Applied Mechanics Reviews. 56(1):B2-B2-B2-B2.

Stewart G.W. 2003. On the powers of a matrix with perturbations. Numerische Mathematik. 96(2):363-376.

Stewart G.W. 2003. Memory leaks in derived types revisited. SIGPLAN Fortran Forum. 22(3):25-27.

Stewart G.W. 2003. Building an Old-Fashioned Sparse Solver. UMIACS-TR-2003-95

2002

Stewart G.W. 2002. Addendum to "A Krylov--Schur Algorithm for Large Eigenproblems". UMIACS-TR-2001-90

2001

Stewart G.W. 2001. Backward Error Bounds for Approximate Krylov Subspaces. UMIACS-TR-2001-32

Stewart G.W. 2001. Matrix Algorithms: Eigensystems.

Stewart G.W. 2001. Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods. UMIACS-TR-2001-31

Stewart G.W. 2001. On the eigensystems of graded matrices. Numerische Mathematik. 90(2):349-370.

2000

Kilmer M, Stewart G.W. 2000. Iterative regularization and MINRES. SIAM Journal on Matrix Analysis and Applications. 21(2):613-628.

Stewart G.W. 2000. A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations. UMIACS-TR-99-78

Li R-C, Stewart G.W. 2000. A new relative perturbation theorem for singular subspaces. Linear Algebra and its Applications. 313(1–3):41-51.

Stewart G.W. 2000. An Arnoldi--Schur Algorithm for Large Eigenproblems. UMIACS-TR-2000-21

Stewart G.W. 2000. The decompositional approach to matrix computation. Computing in Science Engineering. 2(1):50-59.

1999

Stewart G.W. 1999. The QLP Approximation to the Singular Value Decomposition. SIAM Journal on Scientific Computing. 20(4):1336-1348.

Stewart G.W. 1999. On Orthogonalization in the Inverse Power Method. UMIACS-TR-99-64

Stewart G.W. 1999. Four algorithms for the efficient computation of truncated pivoted QR approximations to a sparse matrix. Numerische Mathematik. 83(2):313-323.

Jia Z, Stewart G.W. 1999. An analysis of the Rayleigh-Ritz method for approximating eigenspaces.

1998

Stewart G.W. 1998. Incremental Condition Calculation and Column Selection. UMIACS-TR-90-87

Stewart G.W. 1998. On the Perturbation of LU, Cholesky, and QR Factorizations. UMIACS-TR-92-24

Stewart G.W. 1998. Matrix Algorithms: Basic decompositions.

Stewart G.W. 1998. The Triangular Matrices of Gaussian Elimination and Related Decompositions. UMIACS-TR-95-91

Stewart G.W. 1998. Basic decompositions. 1

Roginsky J, Stewart G.W. 1998. Time-Domain Extraction of Broad-Band Sources by Tikhonov-Phillips Regularization of Triangular Toeplitz Kernels*. UMIACS-TR-95-87

Stewart G.W. 1998. On an Inexpensive Triangular Approximation to the Singular Value Decomposition. UMIACS-TR-97-75

Stewart G.W. 1998. Two Algorithms for the The Efficient Computation of Truncated Pivoted QR Approximations to a Sparse Matrix. UMIACS-TR-98-12

Boman EC, Griffen MF, Stewart G.W. 1998. Direction of Arrival and the Rank-Revealing URV Decomposition. UMIACS-TR-91-166

Stewart G.W. 1998. Two Simple Residual Bounds for the Eigenvalues of Hermitian Matrices. UMIACS-TR-89-123

Stewart M, Stewart G.W. 1998. On hyperbolic triangularization: Stability and pivoting. SIAM journal on matrix analysis and applications. 19(4):847-860.

Schroeder E, Stewart G.W. 1998. On Infinitely Many Algorithms for Solving Equations. UMIACS-TR-92-121

Stewart G.W. 1998. Perturbation Theory for the Singular Value Decomposition. UMIACS-TR-90-124

Stewart G.W. 1998. Four algorithms for the efficient computation of truncated pivoted QR approximation to a sparse matrix. TR-98-12

Stewart G.W. 1998. QR Sometimes Beats Jacobi. UMIACS-TR-95-32

Stewart G.W. 1998. On Sublinear Convergence. UMIACS-TR-95-92

Stewart G.W. 1998. On the adjugate matrix. Linear Algebra and its Applications. 283(1–3):151-164.

Von Matt U, Stewart G.W. 1998. Rounding Errors in Solving Block Hessenberg Systems. UMIACS-TR-94-105

Stewart G.W. 1998. Gaussian Elimination, Perturbation Theory and Markov Chains. UMIACS-TR-92-23

Oleary DP, Stewart G.W. 1998. On the convergence of a new Rayleigh quotient method with applications to large eigenproblems. Electronic Transactions on Numerical Analysis. 7:182-189.

Bai Z, Stewart G.W. 1998. SRRIT--A FORTRAN Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix. UMIACS-TR-92-61

Stewart G.W. 1998. Implementing an Algorithm for Solving Block Hessenberg Systems. UMIACS-TR-94-70

1997

Stewart G.W. 1997. On the Perturbation of LU and Cholesky Factors. IMA Journal of Numerical AnalysisIMA J Numer Anal. 17(1):1-6.

Stewart G.W. 1997. The Triangular Matrices of Gaussian Elimination and Related Decompositions. IMA Journal of Numerical Analysis. 17(1):7-16.

Higham NJ, Stewart G.W. 1997. Accuracy and Stability of Numerical Algorithms. SIAM Review. 39(1):164-165.

Stewart G.W. 1997. On the weighting method for least squares problems with linear equality constraints. BIT Numerical Mathematics. 37(4):961-967.

Chang XC, Paige CC, Stewart G.W. 1997. Perturbation analysis for the QR decomposition. SIAM Journal on Matrix Analysis and Applications. 18:775-791.

Bai Z, Stewart G.W. 1997. Algorithm 776: SRRIT: a Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix. ACM Trans. Math. Softw.. 23(4):494-513.

Stewart G.W. 1997. On markov chains with sluggish transients. Communications in Statistics. Stochastic Models. 13(1):85-94.

1996

Von Matt U, Stewart G.W. 1996. Rounding errors in solving block Hessenberg systems. Mathematics of Computation. 65(213):115-135.

1995

Stewart G.W. 1995. An Iterative Method for Solving Linear Inequalities. CS-TR-1833

Stewart G.W. 1995. On the perturbation of Schur complement in positive semidefinite matrix. TR-95-38

Stewart G.W. 1995. Theory of the Combination of Observations Least Subject to Errors. SIAM, Philadelphia.[Translation of Gauss (1821, 1823, 1826).].

Stewart G.W. 1995. On the solution of block Hessenberg systems. Numerical Linear Algebra with Applications. 2(3):287-296.

Stewart G.W. 1995. On graded QR decompositions of products of matrices. Electronic Transactions on Numerical Analysis. 3:39-49.

Stewart G.W. 1995. On the stability of sequential updates and downdates. Signal Processing, IEEE Transactions on. 43(11):2642-2648.

Stewart G.W. 1995. Gauss, Statistics, and Gaussian Elimination. Journal of Computational and Graphical Statistics. 4(1):1-11.