In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified m...In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.展开更多
This paper is concerlled with the investigation of a twrvparametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is a nonsingular con...This paper is concerlled with the investigation of a twrvparametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is a nonsingular consistently ordered 2-cyclic matrix. We give sufficient and necessary conditions for strong convergence of the MEJ method and we determine the optimum extrapolation parameters and the optimum spectral radius of it, in the case where all the efornvalues of the block Jacobi iteration matrir associated with A are real. In the last section, we compare the MEJ with other known methods.展开更多
基金the National Natural Sciences Foundation of China(10371044)the Science and Technology Commission of Shanghai Municipality through Grant(04JC14031)+1 种基金the University Young Teacher Sciences Foundation of Anhui Province(2006jq1220zd)Supported by the Ph.D.,Program Scholarship Fund of ECNU(2007)
文摘In this paper, the authors discuss the relationship in detail between the rank of M in the modified matrix M = A ＋ BC^＊ and the rank of matrix A. The authors do believe the results are useful tools in the modified matrices.
文摘This paper is concerlled with the investigation of a twrvparametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is a nonsingular consistently ordered 2-cyclic matrix. We give sufficient and necessary conditions for strong convergence of the MEJ method and we determine the optimum extrapolation parameters and the optimum spectral radius of it, in the case where all the efornvalues of the block Jacobi iteration matrir associated with A are real. In the last section, we compare the MEJ with other known methods.
