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Stability of block LU factorization

โœ Scribed by James W. Demmel; Nicholas J. Higham; Robert S. Schreiber

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
975 KB
Volume
2
Category
Article
ISSN
1070-5325

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Stability of block LDLT factorization of
Stability of block LDLT factorization of a symmetric tridiagonal matrix
โœ Nicholas J. Higham ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 358 KB

For symmetric indefinite tridiagonal matrices, block LDL T factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots.