multiple root

This paper brief introduce numerical method of algebraic equation,points out their shortcoming of missing multiple root and put forward one new kind of method--multiple derivation numerical method.

本文对通常代数方程的数值计算方法特点进行了简介并给以分析 ,指出了这些解法无法得出重根数的缺陷 ,提出了一种新的解决方法———多次求导数值计算法 ,使得数值计算法更加清晰、明了 ,且可得出重根数。

The improvement can maintain the speed of the original convergence and is still effective when there are multiple roots.

对牛顿 (Newton)求根公式作了改进 ,使其对重根情况仍有效 ,并保持原有的收敛性

Give out the distinguish theorem of multiple root based on maximum value.

根据导函数的极值分析实根的分布情况、迭代区间和迭代初值,利用三次收敛的迭代方法求解方程的实根,给出了根据极值的重根判别定理。

In order to get the λ repeated roots of equation f(x) = 0, where　λ∈R~+ and the equation may be underivative, an generalized Newton iterative method was constructed with order 2 as its convergence.

设方程f(x)=0有λ重根,其中λ为任意正实数,函数f(x)可能不可导,给出了求这一类方程的λ重根的一个广义Newton迭代法,并证明了这种方法的收敛阶为2。

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.

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 author completely gives the roots of these equations in the F,that is,they have (n,p~k-1)-1 single roots or (n,p~k-1) distinct groups of repeated roots,and they have no root.

本文完整地给出这些方程在F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。

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.

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。

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.

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。

This paper discusses an iteration method for simultaneously finding multiple roots of a polynomial.

讨论一个同时求解多项式重根的迭代法,给出其收敛性定理及其简洁证明,数值结果是满意的。

Effect of seeding-year clipping frequency on root weight and yield in alfalfa and brome grass mixture swards;

刈割对混播草地根重及翌年产草量的响应

Preliminary research on relationship between boron content and root weight and sugar content in sugarbeet root;

甜菜块根中硼元素含量与其根重和含糖率关系的初步研究

Law of ginseng root weight changes during ginseng growth was tested by the field experiment from 1993 to 2001.

通过田间试验,对1993-2001年人参生长过程中根重变化规律进行了研究,并采用数学模拟的方法,对参根增重过程中某些数量规律和特点进行了分析。

Cathodic reaction rate at open circuit Potential for iron in sulfuric acid containing dichromate ion was controlled by both electron transfer process and diffusion process.

铁在含有一定浓度重铬酸根的硫酸中，自腐蚀状态下的阴极反应速率受重铬酸根阴极还原电子转移过程与扩散过程共同控制。

A method was investigated for determination of bicarbonate in water samples by ion chromatography exclusion with conductivity detector.

本文研究了用离子排斥色谱法分析水样品中重碳酸根的最佳色谱条件、分离方式和流动相的选择、样品溶液pH值与峰高的关系,实验结果显示:该方法具有简便、用样量少、灵敏度高和干扰少等优点。

They braced up the wooden bridge with ten heavy posts

他们用10根重柱子将那座木桥支撑

accentual verse

根据重音定节奏的诗行

petition for a retrial in the light of new evidence

根据新证据请求重审.

But candles had to be remade, and water clocks had to be refilled.

但蜡烛总得一根根选，水钟需要重新装满水。

Starch content in root was positively correlation with dry weight of root.

参根淀粉含量与参根干重呈显著正相关。

The root of this plant, formerly an important source of the dye alizarin.

茜草根该植物的根，原为染料茜素的重要来源

The next significant question was how to predict the number of positive, neg ative and complex roots.

次一个重要的问题是怎样预知正根，负根和复根的个数。

According to start of hint, rush one layer after layer toll-gate, beat till the last victory.

根据开始的提示，闯过一重重关卡，打到最后胜利。

The fundamental changes in the machinery of war direction were more real than apparent.

作战指挥机构的根本改变是重实际而不重表面。

The root of Dr Kirby's dark mood, however, was the war.

不过柯比博士心事重重的根源却是战争。

Baggage that does not qualify as free allowance will be charged for at published tariff rates.

超重行李要根据公布的收费单而另加超重费。

That's wholly immaterial to me.

对我来说那根本无足轻重。

It is of small (no) consequence.

这件事没什么（根本不）重要。

14 SOT: JUERGEN KLINSMANN (GERMAN) THIS AXIS IS OF GREAT IMPORTANCE.

于尔根?克林斯曼说：这条轴心非常重要。

She would not even wish for any renewal of his attention.

她甚至根本不希望他再来重修旧好。

Tie a heavy weight at the end of a long piece of string.

把一个重物拴在一根长绳子的一端，

Please resend your request, according to the following instructions.

请重新发送你的请求,根据下列指令.

He walks with the aid of a heavy stick.

他靠着一根笨重的手杖走路。