重根

重根牛顿法受计算误差影响最小，松弛牛顿法次之，标准牛顿法最大。

The experimental errors and truncation of coefficients cause the minimal effect to the multiple root method , the more to the relax and the maximal to the standard Newton ' method .

给出迭代发散的一个判定，并讨论重根情形下迭代的收敛速度和迭代加速。

A criterion for divergence of iteration is given and the covergence speed and covergence acceleration for iteration with multiple root are investigated .

n次多项式有n重根的充要条件

Polynomials of degre n has necessary and sufficient condition of N-ple root

一元n次多项式的重根问题

On the Problem of Fold Root of a Variable Polynomial if Degree N

求一类方程重根的广义Newton迭代法

An generalized Newton iterative method for extracting the roots of a category equation

重根牛顿变换的Julia集

Julia Sets of Newton Method for Multiple Roots

三种牛顿变换Julia集的重根吸引域对α具有敏感的依赖性；

The multiple root attraction region of these kinds of Julia sets are sensitive to a ;

基于Newton迭代法对于求重根具有线性收敛性，给出了加速其收敛的方法以及迭代公式，收敛速度得到了有效的提高。

Considering that the Newton iterative algorithm has first-order convergence in multiple roots , the author advances the method of accelerating its convergence and iteration formula .

本文利用张量分析给出了常系数线性常微分方程组和n阶常系数线性常微分方程初值问题一般解的显式表示，包括特征根有重根时的情况。

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients .

由于∞点不是重根牛顿变换的不动点，故重根牛顿变换的Julia集中多为重根和单根吸引域；

∞ is not the fixed point of multiple roots Newton transform F ( z ), so multiple root 's Julia set is multiple and simple roots attraction region ;

在这里定义了推广的Sturm序列，将Sturm定理进行一定地延拓，给出区间上多项式的所有实根均是偶重根或奇重根的充要条件。

We define the generalized Sturm sequence , and a necessary and sufficient condition for all the roots of polynomials of any degree in given interval have even or odd multiplicity is presented .

完整地给出了这些方程在E中的根的状况：（n，pk-1）-1个单根，（n，pk-1）组互不相同的重根，没有根。

The roots of these equations in the E , are completely given , that is , they have ( n , pk-1 ) - 1 single roots or ( n , pk-1 ) distinct groups of repeated roots , and they have no roots .

计算重根特征向量一阶导数的完备模态法的一种改进

Improved Complete Modal Method for Computing Eigenvector Derivatives at Repeated Eigenvalues

关于计算重根的若干迭代程序

Some iterative processes for computing multiple roots of an equation

求无重根时代数方程根的一种数值迭代方法

An iteration method of finding the roots of algebraic equation without repeated root

然而对重根的情形，相应的工作却少之又少。

But in the case of multiple roots , the situation is reversed .

工程中一种新型的代数方程重根数值计算法

A New Kind of Numerical Method of Algebraic Equation Multiple Roots in Engieering

重拳出击实至名归重根特征灵敏度分析

The heavy fist launches an attack harvests eigen ─ sensitivity analysis with repeated eigenvalues

重根特征向量导数的统一迭代法

Unified iterative method for eigenvector derivative computation

一类同时求多项式全部重根的新的迭代方法

A New Class of Iterative Methods for Simultaneously Finding All Multiple Roots of A Polynomical

不用求高阶导数确定函数方程的重根次数

Determining the Times of Multiple Roots for Function Equations without Calculating the Higher Order Derivatives

同时讨论了重根出现时对算法和结果的影响。

Furthermore , the influence of the results on the appearance of multiple roots has been discussed .

对于求解重根的迭代算法而言，这方面的工作很少。

However , to the iterative method for multiple roots , there is only few work on this field .

但是，同时产生了增根。重根特征灵敏度分析

However , the false roots are produced at the same time . EIGEN ─ SENSITIVITY ANALYSIS WITH REPEATED EIGENVALUES

因此，如何构造出求解方程重根的高阶，尤其最优阶的迭代格式是一项具有挑战性的工作。

So , how to construct a higher-order , especially optimal order , iteration for solving multiple roots is worth studying .

导出各组重根的约束广义逆之间的换算式，从而减少总的计算量。

A formula for finding a constraint generalized inverse from another is derived , by which the total calculation can be notably reduced .

计算具有多组重根的非亏损广义特征值问题特征矢导支配方程特解的混合法

A Mixed Method for Calculating Particular Solutions of Eigenvector Derivative Governing Equations in Nondefective Generalized Eigenproblems with Groups of Repeated Roots Analysis on methods to solve dominated equation formed in FEM

利用单根循环码与重根循环码关系，确定出所有能由短码长的四元循环码构造的线性量子码。

Using the relation of simple root cyclic codes and repeat root cyclic codes , the linear quantum codes that can be constructed from quaternary cyclic codes of short lengths are determined .

主要解决特征重根型的变系数线性非齐次微分方程的两个问题：其一，推广常系数线性非齐次方程的降阶原理；

This article has mainly solved two problems about a kind of nonhomogeneous differential equation with variable coefficients : ( 1 ) It extended the derogatory principle of nonhomogeneous linear equation with constant coefficients .

就一类函数极值与重根的关系作比较深入的探讨，并对这些关系作一些应用研究。

In this paper , the authors deeply discussed the relations between the extremum and the multiple roots for some types of functions , and researched how to use the relations in real world .