(Enter summary)
Abstract: Introduction
The effects of rounding errors on algorithms in numerical linear algebra have
been much-studied for over fifty years, since the appearance of the first digital
computers. The subject continues to occupy researchers, for several reasons.
First, not everything is known about established algorithms. Second, new
algorithms are continually being derived, and their behaviour in finite precision
arithmetic needs to be understood. Third, new error analysis techniques
lead to different... (Update)
Similar documents based on text: More All
2.1: Notes on Accuracy and Stability of Algorithms in Numerical Linear .. - Higham (1998)
(Correct)
1.2: Numerically Stable Generation of Correlation Matrices and.. - Davies, Higham (1999)
(Correct)
1.1: Generating Test Matrices for the One- and Two-Sided Jacobi.. - Davies, Higham (1999)
(Correct)
BibTeX entry: (Update)
@techreport{ higham98notes,
author = "Nicholas J. Higham",
title = "Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra",
number = "No. 333",
address = "Manchester, England",
pages = "42",
year = "1998",
url = "citeseer.ist.psu.edu/article/higham98notes.html" }
Citations (may not include all citations):
313
Matrix Perturbation Theory (context) - Stewart, Sun - 1990
258
Golub and Charles F (context) - Gene - 1996
155
Society for Industrial and Applied Mathematics (context) - Anderson, Bai et al. - 1995
126
Numerical Methods for Least Squares Problems (context) - Bjorck - 1996
102
Jacobi's method is more accurate than QR
- Demmel, Veseli'c - 1992
99
Society for Industrial and Applied Mathematics (context) - Higham, Stability et al. - 1996
95
Numerical Recipes in FORTRAN: The Art of Scientific Computin.. (context) - Press, Teukolsky et al. - 1992
57
Society for Industrial and Applied Mathematics (context) - Dongarra, Bunch et al. - 1979
57
Some stable methods for calculating inertia and solving symm.. (context) - Bunch, Kaufman - 1977
45
Inverse free parallel spectral divide and conquer algorithms..
- Bai, Demmel et al. - 1997
44
Direct methods for solving symmetric indefinite systems of l.. (context) - Bunch, Parlett - 1971
32
Computing the polar decomposition---with applications (context) - Higham - 1986
29
Condition numbers and equilibration of matrices (context) - van der Sluis - 1969
28
Accurate symmetric indefinite linear equation solvers (context) - Ashcraft, Grimes et al. - 1998
27
Society for Industrial and Applied Mathematics (context) - Demmel, Linear - 1997
26
Relative perturbation techniques for singular value problems (context) - Eisenstat, Ipsen - 1972
23
The cyclic Jacobi method for computing the principal values .. (context) - Forsythe, Henrici - 1960
22
Accurate eigensystem computations by Jacobi methods
- Mathias - 1995
22
Inversion of matrices by biorthogonalization and related res.. (context) - Hestenes - 1958
21
Solution of linear equations by diagonalization of coefficie.. (context) - Kogbetliantz - 1955
19
Society for Industrial and Applied Mathematics (context) - Trefethen, Numerical - 1997
17
Some aspects of generalized QR factorizations (context) - Paige - 1990
15
Iterative refinement of linear least squares solutions by Ho.. (context) - Bjorck, Golub - 1967
15
Computing the Singular and the Generalized Singular Values (context) - Drmac - 1994
14
Stability of the diagonal pivoting method with partial pivot..
- Higham - 1997
11
Society for Industrial and Applied Mathematics (context) - Parlett, Eigenvalue - 1998
9
On applying Householder transformations to linear least squa.. (context) - Powell, Reid - 1968
8
Stability of Householder QR factorization for weighted least..
- Cox, Higham - 1997
8
The numerical solution of the general Gauss--Markov linear m.. (context) - Hammarling - 1987
7
Generalized QR factorization and its applications
- Anderson, Bai et al. - 1992
6
Accuracy and stability of the null space method for solving ..
- Cox, Higham - 1997
6
Backward perturbation bounds for linear least squares proble..
- Gu - 1998
6
Compact Numerical Methods for Computers: Linear Algebra and .. (context) - Nash - 1990
6
Society for Industrial and Applied Mathematics (context) - Lawson, Hanson et al. - 1995
5
Iterative methods for equalityconstrained least squares prob.. (context) - Barlow, Nichols et al. - 1988
5
Relative perturbation results for matrix eigenvalues and sin..
- Ipsen - 1998
5
Analysis of algorithms for reflections in bisectors (context) - Parlett - 1971
4
QR factorization with complete pivoting and accurate computa..
- Higham - 1998
4
Partial pivoting strategies for symmetric matrices (context) - Bunch - 1974
3
Row-wise backward stable elimination methods for the equalit..
- Cox, Higham - 1998
3
Implementation of Jacobi rotations for accurate singular val.. (context) - Drmac - 1997
3
A modified Cholesky algorithm based on a symmetric indefinit..
- Cheng, Higham - 1996
3
the reduction of a symmetric matrix to tridiagonal form (context) - Aasen - 1971
3
On sharp quadratic convergence bounds for the serial Jacobi .. (context) - Hari - 1991
2
A note on a one-sided Jacobi algorithm (context) - Veseli'c, Hari - 1989
2
Fast parallelizable methods for the Hermitian eigenvalue pro.. (context) - Zha, Zhang - 1996
2
A comparison of algorithms for solving symmetric indefinite .. (context) - Barwell, George - 1976
1
Symbolic Math Toolbox Version (context) - Moler, Costa - 1997
1
Symmetric Indefinite Matrices: Linear System Solvers and Mod.. (context) - Cheng - 1998
1
Stability of block LDL tridiagonal matrix (context) - Higham - 1997
1
Aasen's method for linear systems with self-adjoint matrices (context) - Hanson - 1997
Documents on the same site (http://webdoc.gwdg.de/ebook/e/2000/mathmanchester/u-manchester-mccm.html): More
Implicit Algorithms and their Linearisation for the.. - Smith, Silvester (1996)
(Correct)
Numerical Hopf bifurcation for a Class of Delay Differential.. - Ford, Wulf (1999)
(Correct)
Continuous Explicit Runge-Kutta Methods for Ordinary and Delay.. - Paul (1994)
(Correct)
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC