G.W. "Pete" Stewart
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.
2011. On the Numerical Analysis of Oblique Projectors. SIAM Journal on Matrix Analysis and Applications. 32(1):309-348.
2009. On the Semidefinite B-Arnoldi Method. SIAM Journal on Matrix Analysis and Applications. 31(3):1458-1468.
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.
2008. Block Gram–Schmidt Orthogonalization. SIAM Journal on Scientific Computing. 31(1):761-775.
2007. Analysis of the Residual Arnoldi Method. UMIACS-TR-2007-45
2007. A Residual Inverse Power Method. UMIACS-TR-2007-09
2006. The Gram-Schmidt Algorithm and Its Variations. UMIACS-TR-2004-84
2006. A note on generalized and hypergeneralized projectors. Linear Algebra and its Applications. 412(2–3):408-411.
2006. EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems. UMIACS-TR-2006-07
2005. Error Analysis of the Quasi-Gram–Schmidt Algorithm. SIAM Journal on Matrix Analysis and Applications. 27(2):493-506.
2005. Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices. ACM Transactions on Mathematical Software-TOMS. 31(2):252-269.
2004. An Elsner-like perturbation theorem for generalized eigenvalues. Linear Algebra and its Applications. 390:1-5.
2004. Error Analysis of the Quasi-Gram--Schmidt Algorithm. UMIACS-TR-2004-17
2003. A Fortran 95 Matrix Wrapper. UMIACS-TR-2003-89
2003. Matrix Algorithms, Volume II: Eigensystems. Applied Mechanics Reviews. 56(1):B2-B2-B2-B2.
2003. On the powers of a matrix with perturbations. Numerische Mathematik. 96(2):363-376.
2003. Memory leaks in derived types revisited. SIGPLAN Fortran Forum. 22(3):25-27.
2003. Building an Old-Fashioned Sparse Solver. UMIACS-TR-2003-95
2002. Addendum to "A Krylov--Schur Algorithm for Large Eigenproblems". UMIACS-TR-2001-90
2001. On the eigensystems of graded matrices. Numerische Mathematik. 90(2):349-370.
2001. Backward Error Bounds for Approximate Krylov Subspaces. UMIACS-TR-2001-32
2001. Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods. UMIACS-TR-2001-31
2000. An Arnoldi--Schur Algorithm for Large Eigenproblems. UMIACS-TR-2000-21
2000. The decompositional approach to matrix computation. Computing in Science Engineering. 2(1):50-59.
2000. Iterative regularization and MINRES. SIAM Journal on Matrix Analysis and Applications. 21(2):613-628.
2000. A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations. UMIACS-TR-99-78
2000. A new relative perturbation theorem for singular subspaces. Linear Algebra and its Applications. 313(1–3):41-51.
1999. Four algorithms for the efficient computation of truncated pivoted QR approximations to a sparse matrix. Numerische Mathematik. 83(2):313-323.
1999. The QLP Approximation to the Singular Value Decomposition. SIAM Journal on Scientific Computing. 20(4):1336-1348.
1999. On Orthogonalization in the Inverse Power Method. UMIACS-TR-99-64
1998. On Sublinear Convergence. UMIACS-TR-95-92
1998. On the adjugate matrix. Linear Algebra and its Applications. 283(1–3):151-164.
1998. Rounding Errors in Solving Block Hessenberg Systems. UMIACS-TR-94-105
1998. Gaussian Elimination, Perturbation Theory and Markov Chains. UMIACS-TR-92-23
1998. On the convergence of a new Rayleigh quotient method with applications to large eigenproblems. Electronic Transactions on Numerical Analysis. 7:182-189.
1998. Implementing an Algorithm for Solving Block Hessenberg Systems. UMIACS-TR-94-70
1998. Incremental Condition Calculation and Column Selection. UMIACS-TR-90-87
1998. On the Perturbation of LU, Cholesky, and QR Factorizations. UMIACS-TR-92-24
1998. The Triangular Matrices of Gaussian Elimination and Related Decompositions. UMIACS-TR-95-91
1998. Basic decompositions. 1
1998. On an Inexpensive Triangular Approximation to the Singular Value Decomposition. UMIACS-TR-97-75
1998. Direction of Arrival and the Rank-Revealing URV Decomposition. UMIACS-TR-91-166
1998. Two Simple Residual Bounds for the Eigenvalues of Hermitian Matrices. UMIACS-TR-89-123
1998. On hyperbolic triangularization: Stability and pivoting. SIAM journal on matrix analysis and applications. 19(4):847-860.
1998. On Infinitely Many Algorithms for Solving Equations. UMIACS-TR-92-121
1998. Perturbation Theory for the Singular Value Decomposition. UMIACS-TR-90-124
1998. QR Sometimes Beats Jacobi. UMIACS-TR-95-32
1997. On the Perturbation of LU and Cholesky Factors. IMA Journal of Numerical AnalysisIMA J Numer Anal. 17(1):1-6.
1997. The Triangular Matrices of Gaussian Elimination and Related Decompositions. IMA Journal of Numerical Analysis. 17(1):7-16.
1997. Accuracy and Stability of Numerical Algorithms. SIAM Review. 39(1):164-165.
1997. On the weighting method for least squares problems with linear equality constraints. BIT Numerical Mathematics. 37(4):961-967.
1997. Perturbation analysis for the QR decomposition. SIAM Journal on Matrix Analysis and Applications. 18:775-791.
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.
1997. On markov chains with sluggish transients. Communications in Statistics. Stochastic Models. 13(1):85-94.
1996. Rounding errors in solving block Hessenberg systems. Mathematics of Computation. 65(213):115-135.
1995. Gauss, Statistics, and Gaussian Elimination. Journal of Computational and Graphical Statistics. 4(1):1-11.
1995. An Iterative Method for Solving Linear Inequalities. CS-TR-1833
1995. Theory of the Combination of Observations Least Subject to Errors. SIAM, Philadelphia.[Translation of Gauss (1821, 1823, 1826).].
1995. On the solution of block Hessenberg systems. Numerical Linear Algebra with Applications. 2(3):287-296.
1995. On graded QR decompositions of products of matrices. Electronic Transactions on Numerical Analysis. 3:39-49.
1995. On the stability of sequential updates and downdates. Signal Processing, IEEE Transactions on. 43(11):2642-2648.