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1.
矩阵方程A^TXB=C的正定和半正定解 总被引:5,自引:1,他引:4
何楚宁 《高校应用数学学报(A辑)》1997,(4):475-480
给出了矩阵方程A^TXB=C在正定和半正定矩阵类中有解的充要条件及解的一般表达式。 相似文献
2.
应用导数的定义,为分段函数的分界点提供了一种行之有效的求导方法,利用微分的定义判断函数在分界点及其他特殊点的可微性,运用定和分的定义求一类特殊类型的极限. 相似文献
3.
调和级数∑n=1^∞1/n是发散的,而极限lim n→∞(∑k=1^∞1/k-lnn)却是收敛的,其极限值称为欧拉常数γ,本文给出了欧拉常数γ的几个有趣的级数表示和积分表示. 相似文献
4.
Research in mathematics and science education reveals a disconnect for students as they attempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular calculus topic that is used frequently in science and engineering: the definite integral. The results of this study demonstrate that certain conceptualizations of the definite integral, including the area under a curve and the values of an anti-derivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sum-based “adding up pieces” conception of the definite integral (renamed in this paper as the “multiplicatively-based summation” conception) is helpful and useful in making sense of a variety of applied integral expressions and equations. Implications for curriculum and instruction are discussed. 相似文献
6.
平均值不等式的矩阵形式 总被引:1,自引:0,他引:1
刘建忠 《纯粹数学与应用数学》2006,22(2):242-246,252
得到了几何—算术平均不等式和几何—调和平均不等式的一些矩阵形式. 相似文献
7.
8.
The concept of a partially separable functionf developed in [4] is generalized to include all functionsf that can be expressed as a finite sum of element functionsf
i
whose Hessians have nontrivial nullspacesN
i
, Such functions can be efficiently minimized by the partitioned variable metric methods described in [5], provided that each
element functionf
i
is convex. If this condition is not satisfied, we attempt toconvexify the given decomposition by shifting quadratic terms among the originalf
i
such that the resulting modified element functions are at least locally convex. To avoid tests on the numerical value of
the Hessian, we study the totally convex case where all locally convexf with the separability structureN
i
1
have a convex decomposition. It is shown that total convexity only depends on the associated linear conditions on the Hessian
matrix. In the sparse case, when eachN
i
is spanned by Cartesian basis vectors, it is shown that a sparsity pattern corresponds to a totally convex structure if and
only if it allows a (permuted) LDLT factorization without fill-in. 相似文献
9.
The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic function. In this paper, we define naturally extended mappings of Lorentzian distance-squared functions, wherein each component is a Lorentzian distance-squared function; and classify these mappings completely by the likeness of recognition subspaces. 相似文献
10.