Gilbert W Stewart Authors: Add personal information
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V. Bibliometrics: Citation Count: 6 As scientific computation continues to scale, it is crucial to use floating-point arithmetic processors as efficiently as possible. Lower precision allows streaming architectures to perform more operations per second and can reduce memory bandwidth pressure on all architectures. However, using a precision that is too low for a given algorithm ... Keywords: Program analysis, Floating-point, Tools, Correctness, Debugging 2 July 2008 ACM Transactions on Mathematical Software (TOMS): Volume 35 Issue 1, July 2008 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 338 Full text available: PDF Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat A of order n ... Keywords: Eigensystem, test matrix generation 3 June 2005 ACM Transactions on Mathematical Software (TOMS): Volume 31 Issue 2, June 2005 Publisher: ACM Bibliometrics: Citation Count: 11 Downloads (6 Weeks): 3,   Downloads (12 Months): 19,   Downloads (Overall): 1,044 Full text available: PDF In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix A . Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant ... Keywords: Gram--Schmidt algorithm, MATLAB, Sparse approximations 4 June 2005 SIAM Journal on Matrix Analysis and Applications: Volume 27 Issue 2, 2005 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 0 Let the $n\,{\times}\,p$ $(n\geq p)$ matrix $X$ have the QR factorization $X = QR$, where $R$ is an upper triangular matrix of order $p$ and $Q$ is orthonormal. This widely used decomposition has the drawback that $Q$ is not generally sparse even when $X$ is. One cure is to discard ... Keywords: QR factorization, Gram--Schmidt algorithm, sparse matrix, orthogonalization, rounding-error analysis 5 December 2003 Numerische Mathematik: Volume 96 Issue 2, December 2003 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 Let A be a matrix of order n . The properties of the powers A k of A have been extensively studied in the literature. This paper concerns the perturbed powers $${{ P_{{k}} = (A+E_{{k}})(A+E_{{k-1}})\cdots(A+E_{{1}}), }}$$ where the E k are perturbation matrices. We will treat three problems concerning the ... 6 December 2003 ACM SIGPLAN Fortran Forum: Volume 22 Issue 3, December 2003 Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 0,   Downloads (12 Months): 4,   Downloads (Overall): 176 Full text available: Pdf In a note in the Fortran Forum , Markus describes a technique for avoiding memory leaks with derived types. In this note, we show by a simple example that this technique does not work when the object in question is a parameter in nested subprogram invocations. A fix is proposed ... 7 February 2002 SIAM Journal on Matrix Analysis and Applications: Volume 24 Issue 2, 2002 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 4 In this addendum to an earlier paper by the author, it is shown how to compute a Krylov decomposition corresponding to an arbitrary Rayleigh quotient. This decomposition can be used to restart an Arnoldi process, with a selection of the Ritz vectors corresponding to that Rayleigh quotient. Keywords: deflation, Krylov sequence, restarting, Arnoldi algorithm, Krylov decomposition, large eigenproblem 8 January 2002 SIAM Journal on Scientific Computing: Volume 24 Issue 1, 2002 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 0 In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon [ Linear Algebra Appl ., 61 (1984), pp. 101--132] shows that the Rayleigh quotient---i.e., the ... Keywords: large eigenproblem, partial reorthogonalization, symmetric matrix, Lanczos method, adjusted Rayleigh quotient 9 September 2001 Bibliometrics: Citation Count: 129 This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats ... 10 March 2001 SIAM Journal on Matrix Analysis and Applications: Volume 23 Issue 3, 2001 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 36 Sorensen's implicitly restarted Arnoldi algorithm is one of the most successful and flexible methods for finding a few eigenpairs of a large matrix. However, the need to preserve the structure of the Arnoldi decomposition on which the algorithm is based restricts the range of transformations that can be performed on ... Keywords: large eigenproblem, deflation, Krylov sequence, restarting, Arnoldi algorithm, Krylov decomposition 11 January 2000 Computing in Science and Engineering: Volume 2 Issue 1, January 2000 Publisher: IEEE Educational Activities Department Bibliometrics: Citation Count: 13 A matrix decomposition is a factorization of a matrix into the product of simpler matrices. The introduction of matrix decomposition into numerical linear algebra in the years from 1945 to 1965 revolutionized matrix computations. This article outlines the decompositional approach, comments on its history, and surveys the six most widely ... 12 October 1999 SIAM Journal on Matrix Analysis and Applications: Volume 21 Issue 2, Oct.-Jan. 2000 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 3 In this paper we present three theorems which give insight into the regularizing properties of MINRES. While our theory does not completely characterize the regularizing behavior of the algorithm, it provides a partial explanation of the observed behavior of the method. Unlike traditional attempts to explain the regularizing properties of ... Keywords: MINRES, iterative regularization, regularization, ill-posed problem 13 February 1999 SIAM Journal on Scientific Computing: Volume 20 Issue 4, July 1999 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 8 In this paper we introduce a new decomposition called the pivoted QLP decomposition. It is computed by applying pivoted orthogonal triangularization to the columns of the matrix X in question to get an upper triangular factor R and then applying the same procedure to the rows of R to get ... Keywords: QLP decomposition, pivoted QR decomposition, rank determination, singular value decomposition 14 October 1998 SIAM Journal on Matrix Analysis and Applications: Volume 19 Issue 4, Oct. 1998 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 5 This paper treats the problem of triangularizing a matrix by hyperbolic Householder transformations. The stability of this method, which finds application in block updating and fast algorithms for Toeplitz-like matrices, has been analyzed only in special cases. Here we give a general analysis which shows that two distinct implementations of ... Keywords: pivoting, triangularization, relational stability, hyperbolic transformation 15 January 1998 Bibliometrics: Citation Count: 0 16 December 1997 ACM Transactions on Mathematical Software (TOMS): Volume 23 Issue 4, Dec. 1997 Publisher: ACM Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 1,   Downloads (12 Months): 10,   Downloads (Overall): 704 Full text available: PDF SRRT is a Fortran program to calculate an approximate orthonomral basis fr a dominant invariant subspace of a real matrix A by the method of simultaneous iteration. Specifically, given an integer m , SRRIT computes a matrix Q with m orthonormal columns and real quasi-triangular matrix T or order m ... Keywords: invariant subspace, nonsymmetric eigenvalue problem, project method 17 October 1997 Bibliometrics: Citation Count: 0 18 October 1997 Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 3 19 July 1997 SIAM Journal on Matrix Analysis and Applications: Volume 18 Issue 3, July 1997 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 6 This paper gives perturbation analyses for $Q_1$ and $R$ in the QR factorization $A=Q_1R$, $Q_1^TQ_1=I$ for a given real $m\times n$ matrix $A$ of rank $n$ and general perturbations in $A$ which are sufficiently small in norm. The analyses more accurately reflect the sensitivity of the problem than previous such ... Keywords: QR factorization, condition estimation, matrix equations, perturbation analysis, pivoting 20 January 1996 Bibliometrics: Citation Count: 0