[數] 正交多項式
In this paper a simplified recursion formula of discretization orthogonal polynomial in the case of uniform step is presented.
給出了離散化正交多項式遞推公式在等距節點情況下的簡化形式。
We have build the multivariate orthogonal polynomial regression forecasting model of the economical effect on winter wheat production.
采用多元正交多項式回歸方法建立了冬小麥生産經濟收益預測的多元正交多項式回歸模型。
The method of orthogonal polynomial regression was used for regression modeling, and then the regression equations and regression coefficients were tested for significance.
采用正交多項式回歸分析法建立回歸模型，并對回歸方程和回歸系數進行顯著性檢驗。
After that, defining modification coefficients of non-orthogonal polynomial basis, Garlekin project scheme is used to set up deterministic nonlinear equations.
第二步，将已獲得的解在非正交多項式基上進行伽遼金投影，通過求解修正系數，來修正原有的計算結果。
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.
提出了一種基于正交函數積分理論的圖像插值快速實現方法，通過構造濾波器沖擊響應的正交多項式函數來确定插值取樣點與插值系數。
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.
利用基于正交多項式的分布拟合方法對實際問題進行了損失分布拟合，取得了較為理想的結果，為損失分布的拟合提供了一種新的方法。
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.
研究了正交多項式回歸在橡膠配方試驗中的應用，并提出了一種基于解釋結構模型的建模方法。
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.
傳統的研究方法是采用多元正交多項式回歸參數優化設計，通過獲得一些經驗公式來進行實驗研究。
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.
提出了描述标準擊實試驗中土料幹密度和含水量之間函數關系的拟合正交多項式方法。
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項式數值逼近方法，提出預測智能控制算法。
The approaches are presented for constructing orthogonal polynomial filter and matrix CQFs.
主要讨論了多項式正交濾波器和共轭正交濾波器組的構造方法。
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.
整個處理過程分為兩步：第一，采用離散正交多項式曲面拟合技術探測邊緣位置；第二，運用松弛标定網突出有意義的邊緣結構和壓縮噪聲邊緣。
Orthogonal polynomial approximation is proposed to estimate the nonlinear deterministic trend and then the residual is used to test the unit root.
本文研究用正交多項式逼近非線性趨勢，然後對殘差進行單位根檢驗的方法。
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.
提出了兩種新的a-N曲線拟合方法：正交多項式法和指數函數法，并給出了參數估計算法。
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.
目前的基于多項式、正交多項式和加權正交多項式的圖像配準方法是以誤差平方和為度量标準的。
Mathematical models and nomograms about the effects were obtained by means of orthogonal polynomial stepwise regressive analysis, and the ergonomical design parameters we…
經模型回歸診斷與回驗率檢驗，表明該研究結果對飛機座艙複合因素環境控制系統工程設計有實用意義。
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項式，逼近梁的位移函數。
Compare the complexity and precision of the polynomial method and orthogonal polynomials method used in geometrical adjustment, an experiment is made;
比較了圖像幾何校正的多項式方法和正交多項式方法在複雜度與精度上的差異，進行了仿真實驗；
The dynamic load identification is formulated by time finite element model with shape function of generalized orthogonal polynomial in this paper.
本文利用廣義正交多項式作為時間有限元的形函數，推導了基于時間有限元的動載荷識别模型。
By using this formula, orthogonal polynomial fitting algorithm for initial value problems of ordinary differential equations is established.
利用這一公式建立了常微分方程初值問題的正交多項式拟合算法。
In this paper, An orthogonal polynomial repression model of non-equidistant points for equal-replicate data was proposed.
本文給出了一種等重複數據情形下的非等距正交多項式回歸模型。
As pline curve has been fitted through interpolating Points that are peak-values evaluated by orthogonal polynomial regression and smoothing maximization.
通過正交多項式回歸及滑動最大法求峰點，作為插值結點來構造樣條曲線。
An orthogonal polynomial decomposition model for the flatness of cold-rolled strip is proposed.
提出冷軋闆形一種構造正交多項式分解模型。
As a kind of complete orthogonal polynomial system, U system has many good properties such as orthogonality and convergence.
作為一種可選定次數的完備正交多項式系統，U系統所定義的矩具有标準正交性、收斂性等優良性質。
First, the orthogonal polynomial regression is used to predict the original value of the machine equipment, and then, the optima!
本文首先應用正交多項式回歸預測了機械設備的原值，然後運用網絡分析法确定了機械設備更新的最優方案；
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.
利用正交多項式序列的正交性及微分算子矩陣，論述了時變非線性分布參數系統參數估計的正交多項式法。
正交多項式（orthogonal polynomial）是數學中一類重要的多項式函數，其核心特性在于它們在特定區間和權重函數下滿足“正交性”條件。以下是詳細解釋：
在函數空間中，兩個多項式 ( P_n(x) ) 和 ( Pm(x) ) 被稱為正交的，如果它們在區間 ([a, b]) 上關于權重函數 ( w(x) ) 滿足： $$ int{a}^{b} P_n(x) P_m(x) w(x) , dx = 0 quad (n eq m) $$ 當 ( n = m ) 時，積分結果為一個非零常數（通常歸一化為1）。這種性質類似于幾何中向量的垂直關系。
不同權重函數和區間對應不同的正交多項式族：
正交多項式可通過Gram-Schmidt正交化過程生成：從标準多項式基 ({1, x, x, ldots}) 出發，在指定内積空間下逐步構造正交基。
正交多項式因其理論深度和實用價值，成為數學物理、工程計算等領域的基礎工具。如需具體應用案例或公式推導，可進一步說明需求。
Orthogonal Polynomial 和 Polynomial 是兩個數學術語。下面将分别介紹這兩個詞的定義、用法、解釋、近義詞和反義詞等。
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