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Abstract: The method of Implicit LU factors for factorizing a nonsingular matrix A, and hence solving systems of equations, is described. It is shown how the factors are related to the regular LU factors computed by Gaussian Elimination. A backward error analysis is given and discussed. Implicit LU factors are shown to be advantageous when a copy of A is kept for other purposes, and particularly so when A is a sparse matrix stored in compact form. It is shown how the method can be implemented efficiently ... (Update)
Context of citations to this paper: More
...for dense systems, and about which there are many relevant papers, yet which is not at all well known. This method is reviewed by Fletcher [3], where many other references are given. It is shown in [3] that implicit LU factors enable systems with both A and A T to be solved,...
Cited by: More
Block Triangular Orderings and Factors for Sparse Matrices in LP - Fletcher (1997) (Correct)
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1.2: A Direct Projection Method For Sparse Linear Systems - Benzi, Meyer (1995) (Correct)
0.6: Recursive Projection and Interpolation Algorithms With Applications - Jbilou (1993) (Correct)
0.5: Optimal Algorithms For Well-Conditioned Nonlinear.. - Bianchini, Fanelli, Gori (Correct)
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BibTeX entry: (Update)
Fletcher R. (1997), Dense Factors of Sparse Matrices, in Approximation Theory and Optimization. Tributes to M.J.D. Powell , (M.D. Buhmann and A. Iserles, eds.), Cambridge University Press. http://citeseer.ist.psu.edu/fletcher97dense.html More
@misc{ fletcher97dense,
author = "R. Fletcher",
title = "Dense Factors of Sparse Matrices",
text = "Fletcher R. (1997), Dense Factors of Sparse Matrices, in Approximation
Theory and Optimization. Tributes to M.J.D. Powell , (M.D. Buhmann and A.
Iserles, eds.), Cambridge University Press.",
year = "1997",
url = "citeseer.ist.psu.edu/fletcher97dense.html" }
Citations (may not include all citations):624 The Algebraic Eigenvalue Problem (context) - Wilkinson - 1965
318 Methods of conjugate gradients for solving linear systems (context) - Hestenes, Stiefel - 1952
176 Introduction to Matrix Computations (context) - Stewart - 1973
70 A sparse approximate inverse preconditioner for the conjugat.. - Benzi, Meyer et al. - 1996
56 Computational Methods of Linear Algebra (context) - Faddeev, Faddeeva - 1963
17 Stability analysis of the method of semi-normal equations fo.. (context) - Bjorck - 1987
12 Notes on the solution of algebraic linear simultaneous equat.. (context) - Fox, Huskey et al. - 1948
6 A direct projection method for sparse linear systems - Benzi, Meyer - 1995
4 A numerically stable form of the simplex algorithm (context) - Gill, Murray - 1973
4 A parallel projection method for linear algebraic systems (context) - Sloboda - 1978
4 A stabilization of the simplex method (context) - Bartels - 1971
4 MOPS -- Mathematical OPtimization System (context) - Suhl - 1994
3 The vector method of solving simultaneous linear equations (context) - Purcell - 1953
2 Terminating and non-terminating iterations for solving linea.. (context) - Householder - 1955
2 Stable modification of explicit LU factors for simplex updat.. (context) - Fletcher, Matthews - 1984
2 A class of direct methods for linear systems (context) - Abaffy, Broyden et al. - 1984
1 Newton's recursive interpolation in IR n (context) - Hegedus - 1986
1 Solving Ax = b: a method with reduced storage requirements (context) - Wassyng - 1982
1 Solving sparse unsymmetric sets of linear equations based on.. (context) - Tuma - 1993
1 Conjugate direction methods for solving linear systems (context) - Stewart - 1973
1 A new method for the solution of Ax = b (context) - Enderson, Wassyng - 1978
1 Projection method (context) - Pietrzykowski - 1960
Documents on the same site (http://www.maths.dundee.ac.uk/~fletcher/):
Nonlinear Programming without a penalty function - Fletcher, Leyffer (2000) (Correct)
On the Asymptotic Behaviour of some New Gradient Methods - Dai, Fletcher (2003) (Correct)
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