分块矩阵的广义逆问题在自动控制领域里有重要的作用,而反三角分块矩阵[C A B O]的群逆存在性和表达式一直是一个未解决的问题.令K是体,Km×n表示K上所有m×n矩阵的集合,M=A[X+YB A B O]是K上一类分块矩阵,其中A,B,X,Y∈Kn×...分块矩阵的广义逆问题在自动控制领域里有重要的作用,而反三角分块矩阵[C A B O]的群逆存在性和表达式一直是一个未解决的问题.令K是体,Km×n表示K上所有m×n矩阵的集合,M=A[X+YB A B O]是K上一类分块矩阵,其中A,B,X,Y∈Kn×n.利用矩阵的分解形式,在矩阵A群逆存在,AX=XA,rank(A)=rank(AX)的条件下,得到了M群逆存在的充分必要条件以及群逆存在时的表达式.展开更多
Based on the PMHSS preconditioning matrix,we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks,and analyze the eigen-properties of the corresponding prec...Based on the PMHSS preconditioning matrix,we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks,and analyze the eigen-properties of the corresponding preconditioned matrices.Numerical experiments show that these rotated block triangular preconditioners can be competitive to and even more efcient than the PMHSS preconditioner when they are used to accelerate Krylov subspace iteration methods for solving block two-by-two linear systems with coefcient matrices possibly of nonsymmetric sub-blocks.展开更多
A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated ...A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.展开更多
文摘分块矩阵的广义逆问题在自动控制领域里有重要的作用,而反三角分块矩阵[C A B O]的群逆存在性和表达式一直是一个未解决的问题.令K是体,Km×n表示K上所有m×n矩阵的集合,M=A[X+YB A B O]是K上一类分块矩阵,其中A,B,X,Y∈Kn×n.利用矩阵的分解形式,在矩阵A群逆存在,AX=XA,rank(A)=rank(AX)的条件下,得到了M群逆存在的充分必要条件以及群逆存在时的表达式.
基金supported by National Natural Science Foundation of China(Grant Nos.11021101 and 91118001)the Hundred Talent Project of Chinese Academy of Sciences and the National Basic Research Program(Grant No.2011CB309703)
文摘Based on the PMHSS preconditioning matrix,we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks,and analyze the eigen-properties of the corresponding preconditioned matrices.Numerical experiments show that these rotated block triangular preconditioners can be competitive to and even more efcient than the PMHSS preconditioner when they are used to accelerate Krylov subspace iteration methods for solving block two-by-two linear systems with coefcient matrices possibly of nonsymmetric sub-blocks.
文摘A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.
