In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen [6], Niu et al. [18] and Xie et al. [25]. Theoretical analysis shows that the new algorithm will converge to the true solution for any initial value under certain assumptions. Finally, three numerical examples are given to verify the eficiency of the accelerated algorithm proposed in this paper.

No abstract

No abstract

a b s t r a c t We study the HSS iteration method for large sparse non-Hermitian positive definite Toeplitz linear systems, which first appears in Bai, Golub and Ng's paper published in 2003 [Z.-Z. Bai, G.H. Golub, M.K. Ng, Hermitian and skew-Hermitian splitting methods for nonHermitian positive definite linear systems, SIAM J. Matrix Anal. Appl. 24 (2003) 603-626], and HSS stands for the Hermitian and skew-Hermitian splitting of the coefficient matrix A. In this note we use the HSS iteration method based on a special case of the HSS splitting, where the symmetric part H = 1 2 (A + A T ) is a centrosymmetric matrix and the skewsymmetric part S = 1 2 (A − A T ) is a skew-centrosymmetric matrix for a given Toeplitz matrix. Hence, fast methods are available for computing the two half-steps involved in the HSS and IHSS iteration methods. Some numerical results illustrate their effectiveness.

No abstract