Solving Hermitian positive definite systems using indefinite incomplete factorizations
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 کاملPositive Definite and Semi-definite Splitting Methods for Non-hermitian Positive Definite Linear Systems
In this paper, we further generalize the technique for constructing the normal (or positive definite) and skew-Hermitian splitting iteration method for solving large sparse nonHermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove th...
متن کاملStrictly Hermitian Positive Definite Functions
Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...
متن کاملModified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems
Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...
متن کاملNew Krylov-subspace Solvers for Hermitian Positive Definite Matrices with Indefinite Preconditioners
Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...
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: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.11.011