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2009.30: Stability of Block LU Factorization

2009.30: James W. Demmel, Nicholas J. Higham and Robert S. Schreiber (1995) Stability of Block LU Factorization. Numerical Linear Algebra with Applications, Vol. 2 (2). pp. 173-190. ISSN 1070-5325 / 1099-1506

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DOI: 10.1002/nla.1680020208


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.

Item Type:Article
Uncontrolled Keywords:block algorithm; MACK; Ievel3 BUS; iterative refinement; LU factorization; backward error analysis; block diagonal dominance
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MIMS number:2009.30
Deposited By:Ms Lucy van Russelt
Deposited On:27 April 2009

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