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1.
李红  刘同波 《大学数学》2008,24(2):128-131
讨论矩阵方程∑k=0^rA^kXB^k=F存在惟一解的充要条件,并给出了两种迭代求解法.  相似文献   

2.
讨论矩阵方程sum from k=0 to r( )A~kXB~k=F存在惟一解的充要条件,并给出了两种迭代求解法.  相似文献   

3.
矩阵方程X-A~*X~qA=Q(q>0)的Hermite正定解   总被引:1,自引:0,他引:1  
本文讨论了矩阵方程X-A*XqA=Q(q>0)的Hermite正定解,给出了q>1时解存在的必要条件,存在区间,以及迭代求解的方法.证明了0相似文献   

4.
本主要研究解矩阵方程AX YB=D和AX XB=D的一种迭代方法.  相似文献   

5.
本文研究矩阵方程X+A*X-qA=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.  相似文献   

6.
研究二次矩阵方程X2-bX-C=O(b>0,C为n×n阶正定阵)的正定解,证明了解的存在唯一性并且给出了求解方法.  相似文献   

7.
矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解   总被引:2,自引:0,他引:2  
本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.  相似文献   

8.
通过构造单调有界迭代序列,研究矩阵方程X-A~*X~(-1)A+B~*X~(-2)B=I的艾米特正定解.给出了方程正定解存在的充分条件及正定解的范围.  相似文献   

9.
矩阵方程X+A~*X~(-q)A=I(q>0)的Hermite正定解   总被引:15,自引:2,他引:13  
1.引言 本文研究矩阵方程 X+A*X-qA=I (1)的Hermite正定解,其中I是一个n×n阶单位矩阵, A是一个n×n阶复矩阵, q是实数且q>0.q=1,q=2时的方程是从动态规划,随机过滤,控制理论和统计学中推导出来的,最近已有许多人对此进行了研究(见参考文献[1,2,4]),本文我们将研究方程(1)的解的存在性和解的性质,并讨论迭代求解及迭代解的收敛性. 对于Hermite矩阵X和Y,文中X≥Y表示X-Y是半正定的,X>y表示X-Y是正定的;对于方阵M,M*表示M的共轭转置,ρ(M)表示M的谱半径,λi(M)  相似文献   

10.
本文利用四元数矩阵方程AX-XB=C有唯一解的充要条件给出了两个定理,并讨论了特殊条件下四元矩阵方程AX-XB=C在C=0和C=0且A=B两种情况下解的性质.  相似文献   

11.
12.
    
The algebra of all matrices over a field has a natural -grading . In this paper graded identities of the -graded algebra over a field of characteristic zero are studied. It is shown that all the -graded polynomial identities of follow from the following:

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13.
-sequences     
A sequence of positive integers is called a -sequence if every integer has at most representations with all in and . A -sequence is also called a -sequence or Sidon sequence. The main result is the following

Theorem. Let be a -sequence and for an integer . Then there is a -sequence of size , where .

Corollary. Let . The interval then contains a -sequence of size , when .

  相似文献   


14.
    
The groups of cobordism classes in the unoriented cobordism group containing a representative admitting a -action with fixed point set of constant codimension are determined.

  相似文献   


15.
    
We compute the -homology for a class of representations of
and which admit a Whittaker model. They are all completely reducible.

  相似文献   


16.
Free     
It has been conjectured that every free algebraic action of the additive group of complex numbers on complex affine three space is conjugate to a global translation. The main result lends support to this conjecture by showing that the morphism to the variety defined by the ring of invariants of the associated action on the coordinate ring is smooth. As a consequence, the graph morphism is an open immersion, and simple proofs of certain cases of the conjecture are obtained.

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17.
The     
ROSSER and SCHOENFELD have used the fact that the first 3,500,000 zeros of the RIEMANN zeta function lie on the critical line to give estimates on and . With an improvement of the above result by BRENTet al., we are able to improve these estimates and to show that the prime is greater than for . We give further results without proof.

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18.
Computing     
Let denote the Von Mangoldt function and . We describe an elementary method for computing isolated values of . The complexity of the algorithm is time and space. A table of values of for up to is included, and some times of computation are given.

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19.
Every -regular     
We prove the following: Theorem A. If is a -regular ultrafilter, then either
(a)
is -regular, or
(b)
the cofinality of the linear order is , and is -regular for all .

Corollary B. Suppose that is singular, and either is regular, or . Then every -regular ultrafilter is -regular.

We also discuss some consequences and variations.

  相似文献   


20.
coefficients     
Let be a system of real smooth vector fields, satisfying Hörmander's condition in some bounded domain (). We consider the differential operator

where the coefficients are real valued, bounded measurable functions, satisfying the uniform ellipticity condition:

for a.e. , every , some constant . Moreover, we assume that the coefficients belong to the space VMO (``Vanishing Mean Oscillation'), defined with respect to the subelliptic metric induced by the vector fields . We prove the following local -estimate:

for every , . We also prove the local Hölder continuity for solutions to for any with large enough. Finally, we prove -estimates for higher order derivatives of , whenever and the coefficients are more regular.

  相似文献   


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