查询词典 polynomial approximation

More than 30 kinds of meshfree methods are reviewed in this paper in the light of weighted residual method, and different meshfree methods can be viewed as different forms of weighted residual method and/or with different approximation functions. Various kinds of meshfree approximate schemes are presented in detail, including moving least square approximation, kernel and reproducing kernel approximation, partition of unity approximation, radial basis approximation, radial point interpolation and natural neighbor interpolation.

详尽介绍了各种无网格近似方案(包括移动最小二乘近似、核近似和重构核近似、单位分解近似、径向基函数近似、点插值近似、自然邻接点插值近似等)和无网格法中常用的各类加权余量法(伽辽金格式、配点格式、局部弱形式、加权最小二乘格式和边界积分格式等)，并讨论了数值积分方法和边界条件的处理等问题。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

The method includes steps: each point in sequence x with length L, i=0, 1, 2,apostrophe L-1 is served as a independent variable of k order polynomial; changing coefficient of polynomial to generate multiple sequence f with length L, where k is nonnegative integer; operation in polynomial is carried out in Galois Field GF, where Q=pm, p as a prime number, and m as nonnegative integer; assigning generated sequences to multiple sectors to set of create biased sequences for each sector; it is different in constant terms of polynomial, and identical to other coefficients of coefficients corresponding to sequence assigned to same sector; creating corresponding time - frequency pattern unit from biased sequences of the sector; repeating TFP unit with equal interval in frequency domain so as to obtain integrated TFP.

本发明涉及一种时频资源的分配方法，所述方法包括：把一个长度为L的序列{x，i＝0，1，2，…L-1}中的每一点作为一个k次多项式的自变量，改变多项式的系数生成多个长度为L的序列{f}，其中k是非负整数，多项式中的运算在伽罗华域GF中进行，其中Q＝p m ，p是一个素数，m是非负整数；把生成的序列分配给多个小区，生成各小区的偏置序列集合，其中分配给同一个小区的序列所对应的生成多项式的常数项不同，其他项的系数都相同；由所述小区的偏置序列生成对应的时频图案单元，将时频图案单元经过频域等间隔重复，得到完整的时频图案。

Finally it mathematically calculates the CRC at bit and byte level and deducts a 16-bit CRC. The calculation and deduction consolidate the CRC theory. Chapter three also introduces the modulation by two, CRC polynomial, reflection polynomial applied in noise environment and the relationship between reflection polynomial and general polynomial.

第三章首先阐述了循环冗余码与循环码的关系——循环冗余码是一种短循环码、循环冗余码具有所有循环码的很多性质；然后，简单介绍循环冗余码的编码、译码原理和实现；最后，从普通数学的角度，分别用按比特、按字节求解CRC，详细推导了校验码宽度为16的CRC的理论过程，进一步为循环冗余码的研究提供有力的理论基础。

A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms.

给出一类非线性系统的实现简单的多项式逼近的建模方法，在此方法中，将输入输出数据通过拓扑同胚变换，变换到[0，1]区间内，用多项式逼近的方法进行建模，对初始给定的多项式模型，通过反复的参数辨识、去除模型中的冗余项，得到非线性系统的多项式逼近模型，再利用拓扑反变换，将数据还原回原始数据区间。

Romberg first use of the method is integral for integration, Then the results obtained by using the interpolation method were obtained Lagrange polynomial interpolation polynomial interpolation and Newton, re-use of least squares fitting of thinking obtained polynomial, the last of these different types of polynomial, identify their respective strengths and weaknesses.

首先运用Romberg积分方法对给出定积分进行积分，然后对得到的结果用插值方法，分别求出Lagrange插值多项式和Newton插值多项式，再运用最小二乘法的思想求出拟合多项式，最后对这些不同类型多项式进行比较，找出它们各自的优劣。

On the basic theory, some concepts are proposed, such as partial derivative of waveform polynomial, waveform polynomial vector, delay matrix, multiple valued Boolean process, conditional sensitization, waveform distance with crosstalk and three-dimentional Boolean process. And based on these concepts, a sensitization theorem for sequential circuits and the transition numbers theorems for waveform polynomial are proposed; the model and data structure for the representation and manipulation of waveform polynomial are proposed.

基础理论方面，提出波形多项式偏导、波形多项式向量、延时矩阵、多值Boolean过程、条件可敏化、考虑串绕的波形距离及三维Boolean过程等概念，并在此基础上提出时序电路的敏化定理、波形多项式描述跳变数的定理以及波形多项式的多项式符号表示与运算的模型和数据结构。

The division with surplus, the comprehensive division and Eisenstein Test applications on polynomial that can not be divided are mainly discussed; the sufficient condition of that polynomial with coefficient being integer has no integer root, that cubic polynomial with coefficient being integer is irreducible in rational domain and that polynomial with coefficient being integer has not two completely same roots are summed up.

主要论述了带余除法、综合除法及不可约多项式艾森斯坦判别法的应用；总结出了整系数多项式的无整数根的充分性，三次整系数多项式在有理数域上不可约的充分性，整系数多项式无重根的充分性。

As an example to cubic trigonometric polynomial Bézier,the characters of trigonometric polynomial Bézier curve is analyzed,and deduced that cubic trigonometric polynomial Bézier curve is more smooth than cubic polynomial Bézier curve.

Bézier曲线是计算机辅助几何设计中的一类重要曲线，文献[1]介绍了三次Bézier曲线插值，文献[2]介绍了三次Bézier曲线的保凸插值，但难以解决一端曲率为0，另一端曲率比较大的插值问题。

Polynomial smooth techniques are applied to SVM model and replace x+ by a very accurate smooth approximation that is Hermite Interpolation polynomial,thus the undifferential model is converted into a differential model.The deduction procedure of Hermite Interpolation polynomial smoothing x+ is extended.

三次Hermite插值多项式光滑的支持向量机模型采用的是一种多项式光滑技术，用三次Hermite插值多项式代替单变量函数x+，将原来不可微的模型变为可微的模型，并且给出了三次Hermite插值多项式光滑化单变量函数x+的推导过程。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。