Factorizing symmetric indefinite matrices
نویسندگان
چکیده
منابع مشابه
Analysis of Block LDL Factorizations for Symmetric Indefinite Matrices∗
We consider the block LDL factorizations for symmetric indefinite matrices in the form LBL , where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been well-studied in the literature. In this paper we give a condition under which the LBL factorization will r...
متن کاملThe Snap-Back Pivoting Method for Symmetric Banded Indefinite Matrices
The four existing stable factorization methods for symmetric indefinite pivoting (row or column exchanges) maintains a band structure in the reduced matrix and the factors, but destroys symmetry completely once an off-diagonal pivot is used. Two-by-two block pivoting maintains symmetry at all times, but quickly destroys the band structure. Gaussian reduction to tridiagonal also maintains symmet...
متن کاملStability analysis of block LDLT factorisation for symmetric indefinite matrices
[September 5, 2008; revised December 6, 2009] We consider block LDLT factorisation for symmetric indefinite matrices in the form LDLT , where L is unit lower triangular and D is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorisation and its application to solving symmetric indefinite linear systems has been well studied. On the other hand, while all...
متن کاملA SYM-ILDL: Incomplete LDL Factorization of Symmetric Indefinite and Skew-Symmetric Matrices
SYM-ILDL is a numerical software package that computes incomplete LDLT (or ‘ILDL’) factorizations of symmetric indefinite and skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by [Li and Saad, Crout versions of ILU factorization with pivoting for sparse symmetric matrices, Transactions on Nu...
متن کاملFactorizing complex symmetric matrices with positive definite real and imaginary parts
Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classes of matrix for which it is known to be safe not to pivot in LU factorization. Block LDLT factorization with the pivoting strategy of Bunch and Kaufman is also considered, and it is shown that for such matrices only 1×...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1976
ISSN: 0024-3795
DOI: 10.1016/0024-3795(76)90071-9