实根

求高次方程所有实根的通用C程序

General C-program for the Real Root of Higher Equation

求代数方程实根界限的VB例程

VB programming for real root boundary of algebraic equation

已经知道，判别矩阵的偶数阶主子式的符号确定了f（x）的相异根（实根、复根）的数目。

It is well known that the even order minors of discrimination matrix determine the number of distinct ( real and complex ) roots of f ( x ) .

有理多项式组的实根分离算法和多项式Liénard系统的焦点量求解算法

An Algorithm for Isolating Real Roots of Rational Polynomial Systems and an Algorithm for Calculating Liapunov Values of Polynomial Li ? nard Systems

第一部分主要讨论了Kac-Moody代数中的一类基本问题，即给定一个实根或虚根，其对应的实根向量和虚根向量该如何表示？

Part I is mainly discussing an elementary problem in Kac-Moody Algebra : how to describe the real and imaginary root vectors corresponding to a given real or imaginary root ?

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 .

对其中所用坐标系数表达式均借助于辅助公式和椭园积分化为便于计算的形式，其积分下限t.用解一般形式的椭球方程最大实根加以讨论。

The expressions with coordinate coefficients have been simplified into forms which are easy to compute with the aid of auxiliary formulas and ellipsoidal integration with the lower limit of integration being 7 , which is discussed by evaluating the biggest real root of ellipsoidal equation of common form .

基于混合计算的非线性代数方程组的实根求解

Finding Real Solutions of Nonlinear Algebraic Equations Based on Symbolic-Numeric Methods

当非线性方程无实根时，提供了两种近似解法，并分析了其误差。

Two approximate calculation methods are offered and their error is analyzed .

三次函数的实根与极值

The real root and maximum value of the cubic function

多项式实根的一种求解方法

A Method for Solving the Real Roots of a Polynomial

实根隔离算法及其在电机中的应用

Real root insulating arithmetic and its application to electric machine

这种求根方法不必先给初值，能求出代数方程的全部实根，且求出的根精度较高。

Roots obtained by this method have higher accuracy .

一个新的多项式实根分离算法

A new algorithm to separate real roots of polynomials

非线性代数方程组实根求解研究现状综述

Survey of Finding Real Roots of Nonlinear Equations

一类随机代数方程实根的平均个数的界

The Bounds of Average Number of Real Roots for a Class of Random Algebraic Equations

用变切线法求方程实根的一种迭代方法

An Iterative Method for Finding the Real Roots of Functional Equation by the Method of Variation Tangent Line

基于多项式实根分离算法的三角化方法及其应用

The Triangularization for Polynomial Systems with Applications in Differential Equations Based on an Algorithm of Real Root Isolation

本文构造了一个求首项系数为1，而其余系数均为相等负实数的多项式方程的最大正实根μ的迭代公式。

In this paper , an iteration formula used for computing the positive root of polynomial equations has been construct-ed.

提出了一种基于神经网络的多项式实根隔离算法。

In this paper , we put forward a method for isolating real roots of polynomial based on neural network .

在复外场平面中，我们根据配分函数的正实根找到了各系统的临界点。

In complex field plane , real and positive roots of the partition function mark the type and location of transition .

另一方面，我们给出了零维分片代数簇实根简单而有效的分离算法。

On the other hand , we give the effective and fast algorithm of real root isolation for zero-dimensional piecewise algebraic variety .

本文给出一个求非线性方程实根的迭代公式，证明了由此产生的迭代叙列的收敛性。

This paper proposes a iterative formula for solution to real roots of nonlinear equations , proves convergence of the iterative series .

该算法主要基于凸多面体内代数簇的计算和一元区间多项式实根的计算来实现。

It is primarily based on the computation of algebraic variety on a given convex polyhedron and the real roots of the univariate interval polynomial .

经线性化处理后用状态空间法求出系统特征方程的根&拉普拉斯算子实根（衰减系数）和虚根（阻尼自然频率）。

After linearizing them , the roots of the characteristic equation is derived , roots in laplacian & ( attenuation coefficient ) and the imaginary-roots ( damping frequency ) .

对一类非线性系统的局部稳定控制问题，首先证明一个四次方程实根判定定理，由此给出一类四次型定号的条件和一类系统局部稳定的充分条件。

In this paper , the local stabilization problem of a class of nonlinear control systems is discussed . A theorem concerning the roots of quartic algebraic equations is proved .

本文探讨了带有多个滞量的二阶中立型方程，证明该方程振动的充要条件是特征方程无实根。

This paper considered a second-order neutral equation with several days , and proved that the equation was oscillatory if and only if its characteristic equation had no real root .

证明了一类具有周期系数的中立型微分差分方程振动的充分必要条件是其相应的特征方程无实根。

In this paper , we prove that all solutions of a certain class of neutral differential equations with periodic coefficients oscillate if and only if their characteristic equations have no real roots .

运用多项式方程根的性质理论及著名的牛顿公式，解决了牛顿公式用于多项式方程时迭代初值的选取，并求出多项式方程的所有实根。

On the basis of the character of the root of polynomial equation and well-known Newton Formula , the paper present a method to extract all real roots of polynomial equation and define initial value of iteration .

该指标舍弃了根据方程实根解的存在条件和雅克比矩阵行列式建立计及负荷电压特性的电压稳定性局部指标的方法，准确地反映了负荷电压特性对系统电压稳定性的影响。

This approach discarded the method of establishing voltage-stability index by the real-root existing conditions of equations or the determinant of Jacobin matrix and the proposed index accurately reflected the influences of static load characteristics on voltage stability .