Electronic Resource
New York, NY [u.a.]
:
Wiley-Blackwell
Numerical Linear Algebra with Applications
2 (1995), S. 173-190
ISSN:
1070-5325
Keywords:
block algorithm
;
LAPACK
;
level 3 BLAS
;
iterative refinement
;
LU factorization
;
backward error analysis
;
block diagonal dominance
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be bounded in terms of the condition number K(A) and the growth factor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric positive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.
Additional Material:
4 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nla.1680020208
Permalink
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
