[数] 正交多项式
In this paper a simplified recursion formula of discretization orthogonal polynomial in the case of uniform step is presented.
给出了离散化正交多项式递推公式在等距节点情况下的简化形式。
We have build the multivariate orthogonal polynomial regression forecasting model of the economical effect on winter wheat production.
采用多元正交多项式回归方法建立了冬小麦生产经济收益预测的多元正交多项式回归模型。
The method of orthogonal polynomial regression was used for regression modeling, and then the regression equations and regression coefficients were tested for significance.
采用正交多项式回归分析法建立回归模型，并对回归方程和回归系数进行显著性检验。
After that, defining modification coefficients of non-orthogonal polynomial basis, Garlekin project scheme is used to set up deterministic nonlinear equations.
第二步，将已获得的解在非正交多项式基上进行伽辽金投影，通过求解修正系数，来修正原有的计算结果。
A new method based on orthogonal polynomial integration theory to realize image interpolation with a reduced and constant complexity and with a good precision is presented.
提出了一种基于正交函数积分理论的图像插值快速实现方法，通过构造滤波器冲击响应的正交多项式函数来确定插值取样点与插值系数。
It is used the fitting methods based on orthogonal polynomial to study a practical problem, and achieved better results, that provide a new method for the loss of distribution fitting.
利用基于正交多项式的分布拟合方法对实际问题进行了损失分布拟合，取得了较为理想的结果，为损失分布的拟合提供了一种新的方法。
This phase stu***s the application of orthogonal polynomial regression in rubber formulation experiment and the application of Interpretive Structural Model in Multi-response Modeling Problems.
研究了正交多项式回归在橡胶配方试验中的应用，并提出了一种基于解释结构模型的建模方法。
The multi-element orthogonal polynomial regression is used for traditional optimization technique of parametric optimum design, and the experimental research is done by some experiential formula.
传统的研究方法是采用多元正交多项式回归参数优化设计，通过获得一些经验公式来进行实验研究。
Fitting orthogonal polynomial method for characterizing the functional relationship between the dry density and moisture content of earth-fill in standard compaction test is presented.
提出了描述标准击实试验中土料干密度和含水量之间函数关系的拟合正交多项式方法。
The predictive intelligent control scheme is proposed, which is based on approximation theory and numerical method of Chcbyshev orthogonal polynomial.
本文基于切比雪夫正交多项式数值逼近方法，提出预测智能控制算法。
The approaches are presented for constructing orthogonal polynomial filter and matrix CQFs.
主要讨论了多项式正交滤波器和共轭正交滤波器组的构造方法。
The whole process can be divided into two steps: First, the method of surface fitting with discrete orthogonal polynomial is applied to detection of edge position.
整个处理过程分为两步：第一，采用离散正交多项式曲面拟合技术探测边缘位置；第二，运用松弛标定网突出有意义的边缘结构和压缩噪声边缘。
Orthogonal polynomial approximation is proposed to estimate the nonlinear deterministic trend and then the residual is used to test the unit root.
本文研究用正交多项式逼近非线性趋势，然后对残差进行单位根检验的方法。
Then, on the basis of theory of Taylor series, an orthogonal polynomial model of a-N curves is proposed to have more polynomial degree, and higher relation coefficient.
提出了两种新的a-N曲线拟合方法：正交多项式法和指数函数法，并给出了参数估计算法。
To correct the image distortions in orthopedic surgery based on the Xray fluoroscopic image, an orthogonal polynomial and a weighted orthogonal polynomial methods are proposed.
目前的基于多项式、正交多项式和加权正交多项式的图像配准方法是以误差平方和为度量标准的。
Mathematical models and nomograms about the effects were obtained by means of orthogonal polynomial stepwise regressive analysis, and the ergonomical design parameters we…
经模型回归诊断与回验率检验，表明该研究结果对飞机座舱复合因素环境控制系统工程设计有实用意义。
Thus the authors use distributed polynomial with orthogonal characteristic for approximating displacement function of the beam;
利用正交特征分布多项式，逼近梁的位移函数。
Compare the complexity and precision of the polynomial method and orthogonal polynomials method used in geometrical adjustment, an experiment is made;
比较了图像几何校正的多项式方法和正交多项式方法在复杂度与精度上的差异，进行了仿真实验；
The dynamic load identification is formulated by time finite element model with shape function of generalized orthogonal polynomial in this paper.
本文利用广义正交多项式作为时间有限元的形函数，推导了基于时间有限元的动载荷识别模型。
By using this formula, orthogonal polynomial fitting algorithm for initial value problems of ordinary differential equations is established.
利用这一公式建立了常微分方程初值问题的正交多项式拟合算法。
In this paper, An orthogonal polynomial repression model of non-equidistant points for equal-replicate data was proposed.
本文给出了一种等重复数据情形下的非等距正交多项式回归模型。
As pline curve has been fitted through interpolating Points that are peak-values evaluated by orthogonal polynomial regression and smoothing maximization.
通过正交多项式回归及滑动最大法求峰点，作为插值结点来构造样条曲线。
An orthogonal polynomial decomposition model for the flatness of cold-rolled strip is proposed.
提出冷轧板形一种构造正交多项式分解模型。
As a kind of complete orthogonal polynomial system, U system has many good properties such as orthogonality and convergence.
作为一种可选定次数的完备正交多项式系统，U系统所定义的矩具有标准正交性、收敛性等优良性质。
First, the orthogonal polynomial regression is used to predict the original value of the machine equipment, and then, the optima!
本文首先应用正交多项式回归预测了机械设备的原值，然后运用网络分析法确定了机械设备更新的最优方案；
New method of parameter estimation for time varying non linear distributed systems is proposed in term of orthogonality of orthogonal polynomial and differential operation matrix.
利用正交多项式序列的正交性及微分算子矩阵，论述了时变非线性分布参数系统参数估计的正交多项式法。
正交多项式（orthogonal polynomial）是数学中一类重要的多项式函数，其核心特性在于它们在特定区间和权重函数下满足“正交性”条件。以下是详细解释：
在函数空间中，两个多项式 ( P_n(x) ) 和 ( Pm(x) ) 被称为正交的，如果它们在区间 ([a, b]) 上关于权重函数 ( w(x) ) 满足： $$ int{a}^{b} P_n(x) P_m(x) w(x) , dx = 0 quad (n eq m) $$ 当 ( n = m ) 时，积分结果为一个非零常数（通常归一化为1）。这种性质类似于几何中向量的垂直关系。
不同权重函数和区间对应不同的正交多项式族：
正交多项式可通过Gram-Schmidt正交化过程生成：从标准多项式基 ({1, x, x, ldots}) 出发，在指定内积空间下逐步构造正交基。
正交多项式因其理论深度和实用价值，成为数学物理、工程计算等领域的基础工具。如需具体应用案例或公式推导，可进一步说明需求。
Orthogonal Polynomial 和 Polynomial 是两个数学术语。下面将分别介绍这两个词的定义、用法、解释、近义词和反义词等。
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