Legendre Polynomials

Analysis and Parameter Estimation of a Linear Time-delay Systems via Shifted Legendre Polynomials

变换的勒让德多项式用于线性延迟系统的分析和参数估计

Orthonormal basis in L2 , Legendre polynomials , basis of trigonometric functions .

正交基在L2，勒让德多项式，三角函数的基础。

An Approximate Method to Solved Optimal Control of Linear Systems Via Legendre Polynomials

利用勒让德多项式求解线性系统最优控制的近似方法

Parameter estimation of stochastic continuous linear systems via Legendre polynomials approximation

随机连续线性系统基于Legendre多项式逼近的参数估计

Numerical Approximation for One Type of Stochastic Differential Equations Based on the Legendre Polynomials

一类随机微分方程的Legendre多项式谱逼近分析

A Constructing Method of Non-linear Discriminating Function Based on MDL Criterion Using Legendre Polynomials

非线性判别函数的基于MDL标准的勒让德多项式构造法

Calculus Formula of Legendre Polynomials and Its Simple Application

Legendre多项式的微积分关系式及其简单应用

The nonlinear approximations based on the modified generating functions of the Legendre polynomials were studied .

讨论了利用变形Legendre多项式母函数的非线性逼近。

This paper demonstrates the generalized Rolle theorem and discussed the zero of Legendre polynomials .

对广义罗尔定理进行了证明，并应用广义罗尔定理讨论了勒让德多项式的零点。

Secondly , we fuse ordinal feature and fingerprint orientation estimated by Legendre polynomials to improve the verification performance .

其次，我们还融合了勒让德多项式估计的指纹方向场特征来提高识别的准确性。

On relationship of Legendre polynomials and Chebyshev polynomials

关于勒让德多项式与契贝谢夫多项式间的关系

In the higher-order MoM , the higher order hierarchical basis functions consisting of the modified Legendre polynomials are of good orthogonality .

所采用的高阶基函数是基于修正勒让德多项式的高阶叠层矢量基函数，具有很好的正交性。

The angular coordinate used a DVR based on Legendre polynomials and the radial coordinates utilized a DVR based on sine basis functions .

角度部分的DVR基组选择勒让德多项式形式，而径向坐标采用正弦函数形式。

Some Identities Involving Legendre Polynomials

关于Legendre多项式的一些恒等式

According to the desired accuracy , we determine the number of terms in the Fourier series and Legendre polynomials , then the Practical simplified formulae are obtained .

根据计算精度要求，确定福里哀级数和勒让德多项式的项数，从而得到实用简化公式。

Moments with the Legendre polynomials as kernel function are called Legendre mo-ments , which forma complete orthogonal set inside the unit circle .

Legendre矩是以Legendre多项式为核函数的矩，在单位圆内Legendre多项式构成了一个完备正交集。

First , using the expansion of shifted Legendre polynomials and the operational matrix of integration , we transform the differential equations to a computationally convenient matrix-algebraic form ;

首先，利用移位勒让德多项式展开和积分运算矩阵，把微分方程化为便于计算机计算的矩阵代数方程形式；

All ordinary polynomials have series expansion of orthogonal polynomials , while Legendre polynomials , Hermite polynomials and Laguerre polynomials are special orthogonal polynomials .

一般多项式都可以展开为正交多项式的级数形式，而勒让德多项式、厄米特多项式和拉盖尔多项式都是典型的正交多项式。

This paper gives an upper bound for the rate of square mean convergence of the Lagrange process on the zeros of the derived function of Legendre polynomials and Tchebycheff polynomials .

本文得到了以Legendre多项式及以Tchebycheff多项式的导数的零点为插值结点组的拉格朗日插值多项式于平方收敛意义下的收敛速度。

A random regression model with Legendre polynomials of age as independent variables was used to estimate the covariance functions by restricted maximum likelihood employing the average information algorithm ( AIREML ) .

配合将年龄的勒让德多项式作为自变量的随机回归模型，用平均信息约束最大似然（AIREML）法估计。

Based on the differential transformation of Legendre polynomials , the statistically uncorrelative model of stochastic continuous linear systems is obtained . and then the parameter estimation algorithm is made by the least - squares principle .

基于Legendre多项式微分变换，导出随机连续线性系统的统计无关逼近模型，然后由最小二乘原理给出参数估计算法。

The nonlinear approximations based on the generating functions of the Legendre polynomials were studied . It was proved that such nonlinear approximations to the Dirac delta function on were convergent . Moreover , the approximate errors was examined .

讨论了利用Legendre多项式母函数的非线性逼近，证明了当这类非线性逼近应用于Diracδ函数时逼近是收敛的，且导出了逼近误差。

This method couples the Picard integral equation formulations , the classical defect and deferred correction methods and Gauss Legendre orthogonal polynomials and the corresponding Gaussian quadrature rules .

该方法综合了Picard积分方程形式，传统的亏损校正方法，GaussLegendre正交多项式及相应的Gauss求积公式。

This paper explains a method of flatness pattern recognition , i.e. utilizes character of three pair of Legendre orthogonal polynomials opposite each other to show six flatness typical patterns , bases on the fuzzy recognition methods of margin of weight hamming distance to making flatness pattern recognition .

利用勒让德正交多项式的三对两两互反特性，来表示六种板形基本模式，提出改进的板形模式识别方法，即提出基于加权海明（hamming）距离差的模糊模式识别。

In this paper , an approximation approach is presented for offsetting curve by approximating the normal curve of the base curve using Legendre least-square polynomials . After computing the perturbed vectors , the offset curve can be obtained by shifting the control points of the base curve .

利用最佳平方逼近的Legendre多项式来逼近基曲线的法矢曲线，计算出各控制顶点的偏移向量，由此产生偏移控制多边形来得到等距曲线的逼近曲线。

We suggest a new method of statistic modeling , in which the first nth central moments of real target 's radar cross section ( RCS ) are used to characterize the target , and the Legendre orthogonal polynomials are used to reconstruct the PDF of the target 's RCS .

本文提出了一种新的统计模型，它以统计量的各阶中心矩来表征目标，然后用Legendre正交多项式系来再现其概率密度函数。

In this paper , a new fast algorithm for computing the Legendre moments of gray-level images is presented . By using the recursive property of Legendre polynomials , the recurrence formulas of 1D Legendre moments can be established .

文章提出了一种灰度图像的Legendre正交矩的快速算法，借助于Legendre多项式的递推公式推导出计算一维Legendre矩的递归公式。