Showing papers by "Zhong-Zhi Bai published in 2002"
TL;DR: In this paper, the authors studied efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-hermitian splitting of the coefficient matrix.
Abstract: We study efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix. These methods include a Hermitian/skew-Hermitian splitting (HSS) iteration and its inexact variant, the inexact Hermitian/skew-Hermitian splitting (IHSS) iteration, which employs some Krylov subspace methods as its inner iteration processes at each step of the outer HSS iteration. Theoretical analyses show that the HSS method converges unconditionally to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the HSS iteration which is dependent solely on the spectrum of the Hermitian part and is independent of the eigenvectors of the matrices involved. Numerical examples are presented to illustrate the effectiveness of both HSS and IHSS iterations. In addition, a model problem of a three-dimensional convection-diffusion equation is used to illustrate the advantages of our methods.
860 citations
TL;DR: In this paper, the authors consider parallel matrix multisplitting methods for solving linear complementarity problem that finds a real vector z ] R n such that Mz + q S 0, z S 0 and z T (Mz+ q ) = 0.
Abstract: We consider parallel matrix multisplitting methods for solving linear complementarity problem that finds a real vector z ] R n such that Mz + q S 0, z S 0 and z T ( Mz + q )=0, where M ] R n 2 n is...
90 citations
TL;DR: In this article, the authors studied the symmetric positive semidefinite solution of the matrix equation where A is a given real m×n matrix, B is a real m × p matrix, and C is a true m×m matric, with m, n, p positive integers.
Abstract: We study the symmetric positive semidefinite solution of the matrix equation AX
1
A
T
+ BX
2
B
T
= C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation D
T
XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.
46 citations
TL;DR: In this article, the convergence properties of nonstationary multisplitting two-stage iteration methods for solving large sparse systems of linear equations are further studied when the coefficient matrices are hermitian positive definite matrices.
21 citations