Growth in Gaussian elimination
American Mathematical Monthly
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
On growth in Gaussian elimination with complete pivoting
SIAM Journal on Matrix Analysis and Applications
Stability of block algorithms with fast level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Matrices with positive definite Hermitian part: inequalities and linear systems
SIAM Journal on Matrix Analysis and Applications
Bunch-Kaufman factorization for real symmetric indefinite banded matrices
SIAM Journal on Matrix Analysis and Applications
Factorizing complex symmetric matrices with positive definite real and imaginary parts
Mathematics of Computation
Perturbation Theory for Factorizations of LU Type through Series Expansions
SIAM Journal on Matrix Analysis and Applications
Hi-index | 7.29 |
The existence of block LU factorization without pivoting for complex symmetric block tridiagonal matrices whose real and imaginary parts are positive definite and every block has the same property is assured. Some properties of the factors of the block LU factorization for this kind of matrices are presented. By the block representation of the factorization, the growth factor proposed by Amodio and Mazzia [P. Amodio, F. Mazzia, A new approach to the backward error analysis in the LU factorization algorithm, BIT 39 (1999) 385-402], sometimes, is less than or equal to 1. Based on the growth factor, an error analysis is also considered and it shows that the factorization is stable under some reasonable assumptions. Finally, a numerical experiment on a model problem is used to verify our results.