一类高次整系数多项式的因式分解法

文中利用五次整系数多项式在其范围内分解时而导出的一元二次方程判别式的整数性质,给出了五次整系数多项式的因式分解方法,从而解决了一类高次整系数多项式的因式分解问题.     

二次多项式因式分解理论及一般方法

说明: 1)本文限定在实数域R上讨论,而这种方法确可以用来解决一般数域P上的二次多项式的因式分解问题。2)只是为了读者更容易理解和掌握这种理论及分解方法,才只讨论三个元的情形,而这     

整系数多项式因式分解的一种新方法

利用整系数多项式与正有理数的对应 ,将多项式因式分解通过对真分数序列筛选的办法求得因式 ,给出了整系数多项式因式分解的一种新方法 .     

二元整系数多项式因式分解的一种理论和算法

我们发现可以把二元多项式盾成系数为一元多项式的一元多项式来进行分解，据此，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算法。这个算法还能很自然地推广成分解多元整系数多项式的算法。     

多元整系数多项式因式分解的一种理论和算法

本文将ｔ（ｔ是大于２的整数）元整系数多项式看成为系数为ｔ－２元整系数多项式的二元多项式，建立了多元整系数多项式因式分解的一种新理论，进而得到了分解多元整系数多项式的一个有力的算法。     

关于多项式因式分解的两个定理

关于多项式因式分解的两个定理彭明海（湖南吉首大学４１６０００）我在《高等代数》教学中，发现下面两个定理，今介绍出来，供同行参考．定理１设ｆ（ｘ）＝ａｎｘｎ＋ａｎ－ａｎ－１ｎ＋…＋（Ｚ［ｘ］表示整系数多项式集合）如果有一个素数ｐ满足条件且则ｆ（ｘ）在有...     

整系数一元三次方程虚根存在的条件

对于整系数一元三次方程f（x）=ax^3＋bx^2＋cx＋d=0（a≠0），由代数基本定理知道，它至少有一个实数根；若有虚根，则它总是成对出现的（即两虚根一定互为共轭复数）．尽管有三次方程的求根公式（即著名的卡丹公式），但使用起来还是比较麻烦的．该方程何时有虚根，仍不易判断．     

二元二次多项式可因式分解的充要条件及其分解公式

对于二元二次多项式ｆ（ｘ，ｙ）＝Ａｘ２＋Ｂｘｙ＋Ｃｙ２＋Ｄｘ＋Ｅｙ＋Ｆ（其中Ａ，Ｂ，Ｃ不全为零），设ｈ＝２ＣＤ－ＢＥＢ２－４ＡＣ，ｋ＝２ＡＥ－ＢＤＢ２－４ＡＣ，Ｆ１＝ｆ（ｈ、ｋ）＝１２Ｄｈ＋１２Ｅｋ＋Ｆ，△＝２ＡＢＤＢ２ＣＥＤＥ２Ｆ＝－２（Ｂ２－４Ａ...     

整系数多项式有理根定理的改进

文章对整系数多项式有理根定理进行了推广和改进．运用本文的定理，可使整系数多项式有理根的寻求变得简便易行．     

Stokes问题的区域分解法

本文主要讨论了Ｓｔｏｋｅｓ问题的非重迭型两仓区域性情形的区域分解算法，首先讨论了连续情形，然后将区域分解算法应用到Ｓｔｏｋｅｓ问题的非协调离散情形。     

A Domain Decomposition Method for Frictional Contact Problem

The bilateral or unilateral contact problem with Coulomb friction between two elastic bodies is considered [1]. An algorithm is introduced to solve the resulting finite element system by a non‐overlapping domain decomposition method. The global problem is transformed to a smaller problem on the contact surface. The solution is obtained by using a successive approximation method, in each step of this algorithm we solve two intermediate problems the first with prescribed tangential pressure and the second with prescribed normal pressure.     

Non-Conforming Domain Decomposition with Hybrid Method

We present a non-conforming domain decomposition technique for solving elliptic problems with the finite element method. Functions in the finite element space associated with this method may be discontinuous on the boundary of subdomains. The sizes of the finite meshes, the kinds of elements and the kinds of interpolation functions may be different in different subdomains. So, this method is more convenient and more efficient than the conforming domain decomposition method. We prove that the solution obtained by this method has the same convergence rate as by the conforming method, and both the condition number and the order of the capacitance matrix are much lower than those in the conforming case.     

关于并行迭代区域分解算法收敛性的注记

本文给出在范数Ⅱ·Ⅱ下的收敛估计,以及相应的最优松驰因子,还讨论了这两种收敛性之间的关系.     

Hamilton-Jacobi-Bellman方程的区域分解算法

对离散Hamilton-Jacobi-Bellman方程提出了一类区域分解算法,并在合理的假设下证明了该算法的单调收敛性,数值结果表明该算法的有效性与准确性．     

A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.     

Decomposition of the Flow Polynomial

The flow polynomials denote the number of nowhere-zero flows on graphs, and are related to the well-known Tutte polynomials and chromatic polynomials. We will show the decomposition of the flow polynomials by edge-cuts and vertex-cuts of size 2 or 3. Moreover by using this decomposition, we will consider what kind of graphs have the same flow polynomials. Another application of the decomposition results is that if a bridgeless graph G does not admit a nowhere-zero k-flow and G has a small vertex- or edge-cut, then a proper bridgeless subgraph of G (a graph minor) does not admit a nowhere-zero k-flow either.     

基于对称化原理的对称区域分裂法

本文利用对称化原理,讨论了一种只需在子区域上计算两个完全独立子问题就可得到原问题解的对称区域分裂法,并用此方法求解线性算子方程和线性透射问题.此方法可作为并行算法在MIMD计算机上使用.     

Non-overlapping Domain Decomposition Method for a Nodal Finite Element Method

A new approach is proposed for constructing nonoverlapping domain decomposition procedures for solving a linear system related to a nodal finite element method. It applies to problems involving either positive semi-definite or complex indefinite local matrices. The main feature of the method is to preserve the continuity requirements on the unknowns and the finite element equations at the nodes shared by more than two subdomains and to suitably augment the local matrices. We prove that the corresponding algorithm can be seen as a converging iterative method for solving the finite element system and that it cannot break down. Each iteration is obtained by solving uncoupled local finite element systems posed in each subdomain and, in contrast to a strict domain decomposition method, is completed by solving a linear system whose unknowns are the degrees of freedom attached to the above special nodes.     

空间半无界区域的非重叠区域分解算法

主要研究了空间一种半无界凹球区域上的区域分解算法.在三维空间自然边界规划的基础上,以三维Dirichlet外边值问题为例,进行的D-N交替算法.并提出了该算法与Richardson迭代法的等价性,并分析其收敛性及其收敛速度与网格参数h无关.同时给出了松弛因子的取值范围.