共查询到20条相似文献,搜索用时 195 毫秒
1.
我们知道,直接展开一个λ-矩阵的行列式,其工作量是很大的。对于多元多项式矩阵(即每个元素为多元多项式的矩阵)的行列式展开,工作量则更为惊人。本文利用多维FFT得到了求多元多项式矩阵行列式的一个简单快速的计算方法,并估计了计算复杂性的上界。 相似文献
2.
将二元多项式看成系数为一元多项式的一元多项式来进行分解,本文建立了二元整系数多项式因式分解的一种理论,提出了一个完整的分解二元整系数多项式的新算法.这个算法能自然地推广到多元整系数多项式的分解中去. 相似文献
3.
Z/mZ上的多元置换多项式 总被引:2,自引:0,他引:2
张起帆 《数学年刊A辑(中文版)》1995,(2)
本文研究了一类典型的模p的多元奇异多项式,得到了它们是模Pl(l>1)的置换多项式的充要条件并给出了一个是模p2的置换多项式但不是模p3的置换多项式的多元多项式例子,从而说明模pl(l>1)的多元置换多项式不能(象一元那样)简化到模p上. 相似文献
4.
《数学的实践与认识》2015,(11)
研究了多元多项式系统的Sylvester结式、Dixon结式以及混合CayleySylvester结式之间是否存在特定关系的问题,利用构造混合结式矩阵的方法证明了在满足一定的条件下,多元多项式系统的这些结式的绝对值都相等.而对于一般的多元多项式系统,也证实了上述这些结式之间仅仅相差一个因子,推广了两变元多项式系统的结论. 相似文献
5.
本文研究了交换环上全矩阵代数的迹恒等式,特别研究了积的迹为零的多项式,它好比矩阵或多项式正交,在现代物理学中有着十分广泛的应用. 相似文献
6.
7.
本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间.给出了广义周期Besov类的一种推广,得到了空间元素的一种表示定理,不仅给出了一种多元周期多项式样条算子.而且证明了所得的结果. 相似文献
8.
本文运用分块矩阵及多元多项式的性质对行列式求值中的Cauchy-Binet 定理与Laplace 定理给出了等价证明. 相似文献
9.
10.
11.
Nikolaos M. Missirlis 《Numerische Mathematik》1984,45(3):447-458
Summary A variety of iterative methods considered in [3] are applied to linear algebraic systems of the formAu=b, where the matrixA is consistently ordered [12] and the iteration matrix of the Jacobi method is skew-symmetric. The related theory of convergence is developed and the optimum values of the involved parameters for each considered scheme are determined. It reveals that under the aforementioned assumptions the Extrapolated Successive Underrelaxation method attains a rate of convergence which is clearly superior over the Successive Underrelaxation method [5] when the Jacobi iteration matrix is non-singular. 相似文献
12.
13.
《Journal of Computational and Applied Mathematics》1988,21(1):119-123
In this note we present an algorithm for the computation of matrix functions, especially the matrix exponential. It is a new application of the so-called ‘elimination method’, which was presented for the scalar case in previous papers (e.g. [5]). 相似文献
14.
A new implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric generalized eigenvalue problems is presented. The new method improves and generalizes the SHIRA method of Mehrmann and Watkins (2001) [37] to the case where the skew-symmetric matrix is singular. It computes a few eigenvalues and eigenvectors of the matrix pencil close to a given target point. Several applications from control theory are presented and the properties of the new method are illustrated by benchmark examples. 相似文献
15.
A technique for the resolution of degeneracy in an Active Set Method for Quadratic Programming is described. The approach generalises Fletcher's method [2] which applies to the LP case. The method is described in terms of an LCP tableau, which is seen to provide useful insights. It is shown that the degeneracy procedure only needs to operate when the degenerate constraints are linearly dependent on those in the active set. No significant overheads are incurred by the degeneracy procedure. It is readily implemented in a null space format, and no complications in the matrix algebra are introduced.The guarantees of termination provided by [2], extending in particular to the case where round-off error is present, are preserved in the QP case. It is argued that the technique gives stronger guarantees than are available with other popular methods such as Wolfe's method [11] or the method of Goldfarb and Idnani [7].Presented at the 14th International Symposium on Mathematical Programming, Amsterdam, August 5–9, 1991. 相似文献
16.
Projection method for solving a singular system of linear equations and its applications 总被引:4,自引:0,他引:4
Kunio Tanabe 《Numerische Mathematik》1971,17(3):203-214
Summary The iterative method for solving system of linear equations, due to Kaczmarz [2], is investigated. It is shown that the method works well for both singular and non-singular systems and it determines the affine space formed by the solutions if they exist. The method also provides an iterative procedure for computing a generalized inverse of a matrix. 相似文献
17.
18.
Stefan A. Sauter 《Numerical Linear Algebra with Applications》1995,2(1):17-28
The incomplete Cholesky decomposition is known as an excellent smoother in a multigrid iteration and as a preconditioner for the conjugate gradient method. However, the existence of the decomposition is only ensured if the system matrix is an M-matrix. It is well-known that finite element methods usually do not lead to M-matrices. In contrast to this restricting fact, numerical experiments show that, even in cases where the system matrix is not an M-matrix the behaviour of the incomplete Cholesky decomposition apparently does not depend on the structure of the grid. In this paper the behaviour of the method is investigated theoretically for a model problem, where the M-matrix condition is violated systematically by a suitable perturbation. It is shown that in this example the stability of the incomplete Cholesky decomposition is independent of the perturbation and that the analysis of the smoothing property can be carried through. This can be considered as a generalization of the results for the so called square-grid triangulation, as has been established by Wittum in [12] and [11]. 相似文献
19.
Computing Google’s PageRank via lumping the Google matrix was recently analyzed in [I.C.F. Ipsen, T.M. Selee, PageRank computation, with special attention to dangling nodes, SIAM J. Matrix Anal. Appl. 29 (2007) 1281–1296]. It was shown that all of the dangling nodes can be lumped into a single node and the PageRank could be obtained by applying the power method to the reduced matrix. Furthermore, the stochastic reduced matrix had the same nonzero eigenvalues as the full Google matrix and the power method applied to the reduced matrix had the same convergence rate as that of the power method applied to the full matrix. Therefore, a large amount of operations could be saved for computing the full PageRank vector. 相似文献
20.
In addition to the known method given in [1],authors provide other three methods to the enumeration of one-vertex maps with face partition on the plane.Correspondingly,there are four functional equations in the enufuntion .It is shown that the four equations are equivalent.Moreover,an explicit expression of the solution is found by expanding the powers of the matrix of infinite order directly.This is a new complement of what appeared in [1]. 相似文献