光滑函数

光滑函数的XB保形插值逼近

Approximation of XB Shape - preserving Interpolation In the Smooth Function

重心插值公式具有极好的数值稳定性，重心插值多项式可以以机器精度逼近任意光滑函数，将Lagrange插值公式改写成重心型公式，得到重心Lagrange插值。

Barycentric interpolation formula has excellent numerical stability , and barycentric interpolation polynomial can be machine-precision approximation of an arbitrary smooth function . Barycentric Lagrange interpolation can be obtained by rewriting Lagrange interpolation formula into barycentric formula .

采用小波取样定理和共轭正交小波变换两种方法进行了Radon变换的反演计算，并对不光滑函数的反演计算进行了深入讨论。

The wavelet theory is used for the analysis of inversion of Radon transform .

Fibonacci求积公式对具有有界混合差分的光滑函数类的误差估计

Error Estimates for Fibonacci Quadrature Formulas for Smooth Classes of Functions with Bounded Mixed Difference

给出了Hilbert空间中非光滑函数和次微分的局部和规则，讨论了这个和规则的应用。

This paper gives the subdifferential local sum rule for the sum of nonsmooth functions in Hilbert space and its application .

在Poisson几何里，由于代数A是指一个Poisson流形上的光滑函数代数，因此作为结合代数，A是可交换的。

In Poisson geometry , A is commutative in associative sense , because A is the algebra of smooth functions on a Poisson manifold .

当将熵函数作为正则项加到拉格朗日函数上，我们得到了逐点逼近于M（x）的光滑函数。经证明，该函数即为指数罚函数。

When adding an entropy function as regularizing term to the Lagrangian function , we obtain a smooth approximate function for M ( x ) , which turns out to be the exponential penalty function .

令S（R）和S~（R）分别表示R上的Schwartz速降光滑函数空间和Schwartz缓增广义函数空间；

Let S ( R ) and S ~ ( R ) be the Schwartz space of rapidly decreasing smooth functions and the space of tempered distributions on R respectively .

对由此得到的积分型光滑函数的性质进行了研究，特别的，澄清了已有一L作中对此光滑函数关于光滑参数单调性的误解。

Especially , we clarify the mistake of monotonicity of this integral smoothing function with the smoothing parameter .

研究了由多变量光滑函数为核所确定的第二类Fredholm积分方程类自适的直接方法的优化，并得到了误差阶的精确估计。

The optimal adaptive directive method of approximate solution for Fredholm integral equations with multivariate differentiable kernals are studied , and the optimal error bound are determined .

C~m中有界域上光滑函数的Bochner-Ono公式

Bochner-Ono Formula for Smooth Functions on Bounded Domain in Space C ~ n

因为在实际中，光学参数通常被假定是常数或分片光滑函数，因此我们设定光学参数的求解范围是有界变差（BV）函数空间。

In practice , the optical parameters are assumed to be piecewise constants or piecewise smooth functions . We seek the optical parameters in the space of functions with bounded variation .

基于黄正海等2001年提出的光滑函数，本文给出一个求解P0函数非线性互补问题的非内部连续化算法.所给算法拥有一些好的特性。

Based on the smooth function given in [ 5 ] , we propose in this paper a non-interior continuation algorithm for solving PO function nonlinear complementarity problems , which possesses a few attracting features .

LMA方法以局部网格最小角函数作为目标函数，也通过模拟的方法解决了一个非光滑函数的优化问题。

The LMA method takes the function of calculating the minimal angle of a local mesh , as the objective function , and solves the non-smooth optimization problem by an analogue process .

在二维空间中，得到一类分片光滑函数积分线旋转变化时的Radon变换的奇性传播规律，由此得到Radon变换相对于角度变量的奇性反演公式。

We study and derive the relation between the singularities of a class functions and the singularities of its Radon transform when the integral lines rotate in two-dimensional space . We give the singularity inversion formulas of Radon transform of the function with respect to the angular variable .

利用具有代数精度的降维展开公式，我们可以针对某些特殊区域，在某些光滑函数类中构造出具有2m-1次代数精度及最小余项估值的边界型求积公式。

By using the expansions , we can construct boundary type cubature formulas with the algebraic precision of degree 2m-1 and the best possible estimates for multiple integrals of a kind of smooth functions over certain regions .

但实际应用中遇到的大多数函数都是非光滑函数。

However , output responses are nonsmooth in most practical applications .

关于低度光滑函数的插值余项

The remainder of interpolation for the functions of low order smoothness

光滑函数的Sobolev&Weiner类利用重取样的最优回复

Optimal recovery of sobolev-weiner class of smooth functions by k-fold sampling

关于光滑函数类上的最优取样

Concerning an Optimal Sampling Problem for Some Classes of Smooth Functions

分段光滑函数的带权有理逼近

On Approximation of Piecewise Smooth Functions with Weights by Rational Functions

支持向量机一阶多项式光滑函数的唯一性分析

Uniqueness of 1st-order Polynomial Smooth Function for Support Vector Machines

混合光滑函数类的双曲波逼近

Approximation of multivariate functions with a certain mixed smoothness by hyperbolic wavelet

非光滑函数任意精度光滑逼近的存在性

The Existence of Smooth Approximation for Non smooth Function

投影映射的一种光滑函数

A Smoothing Function for Projection Operator At First Sight

一类非光滑函数的区间扩张

The Inclusion Function for A Class of Nonsmooth Function

非光滑函数的格林公式、高斯公式和斯托克斯公式

Green 's Formula , Gauss 's Formula and Stokes 's Formula of Nonsmooth Functions

光滑函数芽关于右等价群有限决定的一个注记

A Note on Finite Determinacy of Smooth Function-germs with Respect to Right Equivalence Group

三角形内插线曲线光滑函数

Smoothing curve method of plugging line inside triangle

单调光滑函数的样条插值

On spline interpolation for monotone smooth function