逼近

Nonseparable biorthogonal wavelets based on Checkerboard lattice is studied, and the upper bounds of approximation order and smoothness order of the corresponding scaling function are also proved.

研究了一类基于Checkerboard格点的不可分双正交小波，并证明了其尺度函数逼近阶与光滑性的上界。

Applying the triangular element to the stationary Stokes equation, we obtain error analysis and optimal convergent order of approximation solution.

对于各向异性三角形元和各向异性四面体元，我们分别讨论了它们的各向异性插值，将它们应用于定常Stokes方程，我们研究了有限元空间不满足散度条件的各向异性非协调有限元解法，同样得到了逼近解的误差分析和最优收敛阶。

Of course, this conversion between the old and the new CQFs can change the compactly supported, the regularity and the approximation order of the corresponding scaling function. However, for its appliction in signal processing, both the new and the old CQFs can produce identical output for a given input signal.

这种新旧CQFs转化将改变相对应的尺度函数的紧支撑性，正则性和逼近阶等，而在信号处理的过程中，对某一信号而言，用新旧两种CQFs作用可以产生同样的输出信号。

The idea is to add some lower degree terms in the remainder of orthogonal expansion in an element so that the remainder satisfies more orthogonality conditions in the element, and get a desired superclose funtion uI to finite element solution uh.

简述了有限元超收敛研究的一种新想法，即在单元正交展开的余项中添加若干待定低次项，使此余项在一个单元上满足更多的正交性条件，并得到所需的超接近于有限元解uh的逼近函数uI。

Summary In this paper, a brief history review of works on the theory of electromagnetic flowmeters is given. A method named'Alternative iteraction method for approaching real boundaries'is presented to solve Laplace's equation with mixed boundary conditions in electromagnetic flowmeters. The orthogonal expansion is used to analyze weight vectors and flow distribition effects on the sensitivity of the flowmeters.

本文在总结和分析了前人在电磁流量计变送器方面的理论研究成果后，首次提出了"交替迭代逼近边界"的方法求解电磁流量计理论研究中遇到的Laplace方程的混合边界条件问题；采用正交函数展开的方法研究权函数以及被测流体速度分布不规则对仪表输出的影响；采用保角变换的方法首次求解出电磁流量计偏心环域上的权函数。

To deal with data containing time drift, orthogonal polynomials fitting instead of least squares method is used.

研究了一种适用于这种过程的数据处理方法，利用权函数为1的特殊正交多项式做最佳平方逼近，从而避免求解病态方程组，得到较好的处理结果。

The main purpose of this work is to develop the spectral methods associated with some orthogonal systems of polynomials in unbounded domains.

本文正是在这样的背景下提出了无界区域中的谱方法。这种解法是与无界区域中的正交多项式密切相关的。我们的研究由以下几部分组成：第二章，建立了Hermite多项式插值逼近。

This method approximates the nonlinear dynamics efficiently, which is mainly composed of friction in system, by orthogonal polynomials.

该方法利用正交多项式实现对系统中以摩擦力为主的非线性动态充分逼近与补偿，不要求任何摩擦力模型。

This method appro ximates the no nlinear dynamics efficiently, which is mainly composed of friction in system, by orthogonal polynomials.

该方法利用正交多项式实现对系统中以摩擦力为主的非线性动态充分逼近与补偿，不要求任何摩擦力模型。

It is a feature that a sequence of orthogonal Ritz vectors is generated automatically based on the error minimization and employed to reduce the size of the system.

本文以典型的大跨圆拱屋盖为例，将里兹向量直接叠加法应用于屋盖系统特徵值问题计算和风致响应分析，其特点是在误差逼近的基础上自动生成一组正交的里兹向量幷用于缩减系统自由度数。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。