1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive defi...1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on展开更多
A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-m...A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.展开更多
To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the es...To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the estimations for determinants of Dashnic-Zusmanovich type matrices are studied.For a Dashnic-Zusmanovich type matrix,we transform it into a diagonally dominant matrix by using scaling matrices.Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix.Numerical examples are given to illustrate the effectiveness of the proposed results.展开更多
By using a continuous transition method of a matrix and the estimate for spectral radius of a sub-matrix etc., decision methods for a generalized H-matrix under positive definite matrix conditions are researched. Some...By using a continuous transition method of a matrix and the estimate for spectral radius of a sub-matrix etc., decision methods for a generalized H-matrix under positive definite matrix conditions are researched. Some new sufficient conditions for generalized H-matrices are obtained. When a block matrix degenerates a point matrix, these conditions namely become sufficient conditions of H-matrix.展开更多
基金The second author is supported by Xiamen University,China
文摘1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on
基金Foundation item: This work is supported by the Science Foundations of the Education Department of Yunnan Province (03Z169A)the Science Foundatons of Yunnan University (2003Z013B).
文摘A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.
基金supported by the National Natural Science Foundation of China(No.12171323)the Natural Science Foundation of Guangxi Province(No.2023GXNSFAA026514)。
文摘To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the estimations for determinants of Dashnic-Zusmanovich type matrices are studied.For a Dashnic-Zusmanovich type matrix,we transform it into a diagonally dominant matrix by using scaling matrices.Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix.Numerical examples are given to illustrate the effectiveness of the proposed results.
基金Project supported by the National Natural Science Foundation of China (No.10671164)Hunan Provice Key Laboratory for Computation and Simulation in Science and Engineering
文摘By using a continuous transition method of a matrix and the estimate for spectral radius of a sub-matrix etc., decision methods for a generalized H-matrix under positive definite matrix conditions are researched. Some new sufficient conditions for generalized H-matrices are obtained. When a block matrix degenerates a point matrix, these conditions namely become sufficient conditions of H-matrix.
