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101.
1.引言考虑线性方程组TNx=b(1.1)其中TN=(ti,j)是NxN对称正定(SPD)Toeplitz矩阵,即ti,j=t|i-j|(i,j=0,1,...,N-1)且TN的所有特征值均为正数,并表为TN:=T(t。,ti,...,tN-1).如果我们用预条件子共轭梯度法(PCG)求解方程组(1.1),最关健的任务是构造出高效的预条件子.而预条件子最自然的选择似乎其逆矩阵易求且构成矩阵TN的某种最优逼近.由于循环矩阵CN的逆矩阵CR'仍为循环矩阵,因此CN和CH'与向量的乘积可通is速Fourier… 相似文献
102.
We give an example of a -normal space which is not densely normal.
103.
Given a continuous P0-function F : Rn Rn, we describe a method of constructing trajectories associated with the P0-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P0-function lead to P0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P0-equations when the underlying function is P0. To generate the trajectories, we perturb the given P0-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem. 相似文献
104.
Let T be a monad over a category A. Then a homotopy structure for A, defined by a cocylinder P : A A, or path-endofunctor, can be lifted to the category A
T
of Eilenberg–Moore algebras over T, provided that P is consistent with T in a natural sense, i.e. equipped with a natural transformation : T P P T satisfying some obvious axioms. In this way, homotopy can be lifted from well-known, basic situations to various categories of algebras for instance, from topological spaces to topological semigroups, or spaces over a fixed space (fibrewise homotopy), or actions of a fixed topological group (equivariant homotopy); from categories to strict monoidal categories; from chain complexes to associative chain algebras. The interest is given by the possibility of lifting the homotopy operations (as faces, degeneracy, connections, reversion, interchange, vertical composition, etc.) and their axioms from A to A
T
, just by verifying the consistency between these operations and : T P P T. When this holds, the structure we obtain on our category of algebras is sufficiently powerful to ensure the main general properties of homotopy. 相似文献
105.
Kh. D. Ikramov 《Mathematical Notes》1996,60(6):649-657
LetR be a (real or complex) triangular matrix of ordern, say, an upper triangular matrix. Is it true that there exists a normaln×n matrixA whose upper triangle coincides with the upper triangle ofR? The answer to this question is “yes” and is obvious in the following cases: (1)R is real; (2)R is a complex matrix with a real or a pure imaginary main diagonal, and moreover, all the diagonal entries ofR belong to a straight line. The answer is also in the affirmative (although it is not so obvious) for any matrixR of order 2. However, even forn=3 this problem remains unsolved. In this paper it is shown that the answer is in the affirmative also for 3×3 matrices. 相似文献
106.
AJudgingMethodforNormalFamily¥ZhuZhenxing(Dept.ofSystemScienceandMath.,ZhengzhouUniversity,Zhengzhou,450052)Abstract:In1964,H... 相似文献
107.
M. Nussbaum 《Journal of multivariate analysis》1984,14(3):300-314
We consider estimation of the parameter B in a multivariate linear functional relationship Xi=ξi+ξ1i, Yi=Bξi+ξ2i, i=1,…,n, where the errors (ζ1i′, ζ2i′) are independent standard normal and (ξi, i
) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n−1/2 is also established. 相似文献
108.
In this paper we study the families of ETOL and EOL array languages. Standard forms for ETOL and EOL array systems are defined
and closure properties of the families are studied. Relations of these families with other developmental array languages and
other array languages are studied. 相似文献
109.
Anders Rygh Swensen 《Stochastic Processes and their Applications》1983,15(2):181-191
In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation. 相似文献
110.
M.R. Leadbetter G. Lindgren H. Rootzén 《Stochastic Processes and their Applications》1978,8(2):131-139
The asymptotic distribution of the maximum Mn=max1?t?nξt in a stationary normal sequence ξ1,ξ,… depends on the correlation rt between ξ0 and ξt. It is well known that if rt log t → 0 as t → ∞ or if Σr2t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time. 相似文献