Regular incomplete factorizations of real positive definite matrices
نویسندگان
چکیده
منابع مشابه
Solving Hermitian positive definite systems using indefinite incomplete factorizations
Incomplete LDL factorizations sometimes produce an indefinite preconditioner evenwhen the input matrix is Hermitian positive definite. The two most popular iterative solvers for symmetric systems, CG and MINRES, cannot use such preconditioners; they require a positive definite preconditioner. One approach, that has been extensively studied to address this problem is to force positive definitene...
متن کاملA robust incomplete factorization preconditioner for positive definite matrices
We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive de nite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A-orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modi cation. When used in conjunction with the conjugate gradient a...
متن کاملAn Incomplete Cholesky Factorization for Dense Symmetric Positive Definite Matrices
In this paper, we study the use of an incomplete Cholesky factorization (ICF) as a preconditioner for solving dense symmetric positive definite linear systems. This method is suitable for situations where matrices cannot be explicitly stored but each column can be easily computed. Analysis and implementation of this preconditioner are discussed. We test the proposed ICF on randomly generated sy...
متن کاملOn Factorizations of Totally Positive Matrices
Different approaches to the decomposition of a nonsingular totally positive matrix as a product of bidiagonal matrices are studied. Special attention is paid to the interpretation of the factorization in terms of the Neville elimination process of the matrix and in terms of corner cutting algorithms of Computer Aided Geometric Design. Conditions of uniqueness for the decomposition are also given.
متن کاملON f-CONNECTIONS OF POSITIVE DEFINITE MATRICES
In this paper, by using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use α-arithmetic, α-geometric and α-harmonic operator means.
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: 1982
ISSN: 0024-3795
DOI: 10.1016/0024-3795(82)90101-x