计算多项式

Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

本文先叙述了对最小多项式和特征多项式的国内外的研究历史和现状，然后给出了已有的计算常数矩阵特征多项式、多项式矩阵的特征多项式和常数矩阵最小多项式的主要算法及其复杂性。

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

讨论4种常用正交多项式在拟合卫星轨道与时间函数时的适用性；通过计算实例说明利用切比雪夫多项式和勒让德多项式做数据拟合时具有很高的精度；分析得出评定多项式拟合数据精度的适用阶数，实际应用中可降低工作量，提高计算效率；最后讨论同一多项式阶数下不同历元数对拟合结果的影响。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

Therefore,we know that under the mean of statistics, interpolation operators are not only ideal algorithm for realizing optimal approximation polynomials computation,but also ideal computing tool for realizing optimal information- based operation,and the property of their recover functions are good.

这说明了在统计学意义下，插值多项式算子一方面是实现最佳逼近多项式计算的理想算法，另一方面(来源：ABCdd论文网www.abclunwen.com)是实现最优信息基算法的理想计算工具，且具有性质优良的恢复函数。来源：AB03c303C论文网www.abclunwen.com

It takes the function made up of Legendre orthogonal polynomial as displacement function, and use Galerkin method to solve this function. The methods calculating formulas is very simple, so the method can avoid the great calculating difficulty of traditional simplified methods.

正交多项式伽辽金法选取由勒让德正交多项式组成的函数作为位移函数，利用伽辽金法进行求解，计算公式简单，避免了一般简化计算方法由于计算公式的复杂所带来的计算困难。

Finally, we present an efficient algorithm for computing the minimal polynomial of a polynomial matrix. It determines the coefficient polynomials term by term from lower to higher degree.

最后，我们给出了一种计算多项式矩阵最小多项式或特征多项式的有效算法，它从低次项到高次项逐项确定最小多项式的系数多项式。

Nonlinear equation of a polynomial f = 0 in solving problems, I numerical analysis courses designed to do a procedure...

计算多项式非线性方程f=0的求根问题，本人数值分析课程设计做的一个程序，供大家参考，希望给予指正。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Babai, a more accurate estimate vector can be obtained and the coefficients of the multiple polynomial of the interpolation polynomial can be computed.

利用L.Babai最近向量格归约算法得到更精确的估计向量，再计算出插值多项式的倍数多项式的系数，从而计算出原插值多项式的系数。

If Pentium 4 used to be the master of all games built on Quake3 engine, now the situation has changed completely.

如果奔腾4使用的是掌握所有游戏建立在求苛刻的发动机，现在的情况已完全改变。

No, this is not what we mean by framing, although the principle is the same.

不，这不是我们所讲的框架的含义，尽管法则是一样的。