Stability analysis of block LU factorization for complex symmetric block tridiagonal matrices

摘要

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.