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71.
Vladimir Bolotnikov 《代数通讯》2017,45(2):575-599
We introduce the notion of a confluent Vandermonde matrix with quaternion entries and discuss its connection with Lagrange–Hermite interpolation over quaternions. The formula for the rank of a confluent Vandermonde matrix is obtained as well as the representation formula for divided differences of quaternion polynomials. Extensions of these results to the power series setting include the formula for the rank of a confluent Cauchy matrix and norm-constrained Lagrange–Hermite interpolation by square summable power series over quaternions. 相似文献
72.
Let p be a prime number and let be the Vandermonde matrix with -entry equal to for , where ω is a primitive pth root of unity in the complex field. The classical Chebotarëv theorem says that all square submatrices of have nonzero determinant. In this paper, we establish the Chebotarëv theorem over finite fields by imposing certain conditions. 相似文献
73.
74.
Wenchang Chu 《代数通讯》2013,41(8):3619-3633
Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent six using substantial computations which we explain. 相似文献
75.
Given a set TGF(q), |T|=t, wT is defined as the smallest positive integer k for which ∑yTyk≠0. It can be shown that wTt always and wTt−1 if the characteristic p divides t. T is called a Vandermonde set if wTt−1 and a super-Vandermonde set if wT=t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometries. In this paper we classify small and large super-Vandermonde sets. 相似文献
76.
Ren-Cang Li. 《Mathematics of Computation》2008,77(261):335-352
The conjugate gradient (CG) method is widely used to solve a positive definite linear system of order . It is well known that the relative residual of the th approximate solution by CG (with the initial approximation ) is bounded above by
with
where is 's spectral condition number. In 1963, Meinardus (Numer. Math., 5 (1963), pp. 14-23) gave an example to achieve this bound for but without saying anything about all other . This very example can be used to show that the bound is sharp for any given by constructing examples to attain the bound, but such examples depend on and for them the th residual is exactly zero. Therefore it would be interesting to know if there is any example on which the CG relative residuals are comparable to the bound for all . There are two contributions in this paper: - A closed formula for the CG residuals for all on Meinardus' example is obtained, and in particular it implies that the bound is always within a factor of of the actual residuals;
- A complete characterization of extreme positive linear systems for which the th CG residual achieves the bound is also presented.
77.
文章讨论了到复射影空间PN (C)的全纯曲线交超平面的问题,借助Vandermonde行列式, 构造了一些具有N+1个例外超平面的非线性退化的全纯曲线和具有2N个例外超平面的线性退化的非常映射全纯曲线,说明了 Nochka 的全纯曲线的第二基本定理是最优的.最后还构造了具有2N个例外值的N值非常数代数体函数. 相似文献
78.
79.
Vandermonde矩阵的逆模与大系统的分散镇定性 总被引:4,自引:0,他引:4
金朝永 《高校应用数学学报(A辑)》1997,(2):219-228
本文首先给出一种计算Vandermonde矩阵逆模的简单方法,并利用其计算结果对线性定常大系统的分散镇定性进行分析,得到了一个使大系统分散镇定的充分条件及相应的镇定算法同传统的方法相比,我们不仅考虑了关联矩阵的结构,也同时考虑了它的模,且容易计算,便题分析表明本文提供的判断方法具有较少的保守性。 相似文献
80.
设N(x)=为定义在复平面C上的函数.V(x1,…xn)为n×n矩阵,其i行,j列的元素为N(xh).小本给出行列式detV(x1,…xb)≠0的另一种证明. 相似文献