By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive definite systems of linear equations. Theoretical analysis shows that the PSS method converges

No abstract

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper. By fully exploiting the structure of the tensor equation, we propose a projection method based on the tensor format, which needs less flops and storage than the standard projection method. The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product (NKP) preconditioner, which is easy to construct and is able to accelerate the convergence of the iterative solver. Numerical experiments are presented to show good performance of the approaches.National Natural Science Foundation of China [10961010]; Science and Technology Foundation of Guizhou Province [LKS[2009]03