In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
SDD_(k)matrices are a subclass of the nonsingular H-matrices.The infinity norm of the inverse for SDD_(k)matrices has been given.In the paper,we utilize this result in the context of the linear complementarity problem...SDD_(k)matrices are a subclass of the nonsingular H-matrices.The infinity norm of the inverse for SDD_(k)matrices has been given.In the paper,we utilize this result in the context of the linear complementarity problem,and the error bounds of the linear complementarity problem for SDD_(k)matrices are obtained.By the relationship between the SDD matrices and the SDD_(k)matrices,we further obtain the error bounds of the linear complementarity problem for SDD matrices.In addition,it is proved that the bounds presented in this paper are sharper than the well-known bounds under some conditions.Finally,numerical examples are provided to demonstrate the effectiveness of our results.展开更多
We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigen...We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金supported by the Natural Science Foundation of Shaanxi Province,China(Grant No.2020JM-622)the Postgraduate Innovative Research Project of Baoji University of Arts and Sciences(Grant No.YJSCX25YB39).
文摘SDD_(k)matrices are a subclass of the nonsingular H-matrices.The infinity norm of the inverse for SDD_(k)matrices has been given.In the paper,we utilize this result in the context of the linear complementarity problem,and the error bounds of the linear complementarity problem for SDD_(k)matrices are obtained.By the relationship between the SDD matrices and the SDD_(k)matrices,we further obtain the error bounds of the linear complementarity problem for SDD matrices.In addition,it is proved that the bounds presented in this paper are sharper than the well-known bounds under some conditions.Finally,numerical examples are provided to demonstrate the effectiveness of our results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11771046,12101186)Beijing Natural Science Foundation(Grant No.1254039).
文摘We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
