求N次方根(N√A)近似值的一个简捷方法

介绍利用递推式数列求N次方根N√A近似值的一个方法，并利用单调有界原理证得该递推式的收敛性。     

RECONSTRUCTING TRIANGLES INSCRIBED IN CONVEX BODIES FROM X-RAY FUNCTIONS

This paper provides a method using fixed-point theory for the reconstruction of the triangle inscribed in convex bodies from X-ray functions in three arbitrary mutual directions.     

无理数指数幂的底为什么要大于零?

问题的提出经浙江省中小学教材审定委员会审查通过,由浙江教育出版社出版,与人教版普通高中课程标准实验教科书《数学1》相配套的《作业本》第26页,有如下题目:     

"精确到"与"精确度"

新教材引入了二分法求函数的近似值,这就涉及到近似计算中的两个概念:"精确到"与"精确度".教材上用的是精确度,一般如精确度为0.1,是指函数f(x)在区间[a,b]上,有f(a)·f(b)<0,则在(a,b)上存在零点,如∣a-b∣<0.1,在区间上任取一点,包括两个端点,其精确度即为0.1.而"精确到",以精确到0.1为例,即我们平常所说的精确到小数点后一位,是指与精确值的误差不超过±0.05.     

Least-square Solutions of Inverse Problems for Anti-symmetric and Skew-symmetric Matrices

The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.     

A way of constructing translation network operators by Bernstein operators

In the present paper,we provide a way of constructing translation network operators by Bernstein-Durrmeyer operators.     

Adaptive Algorithms of Nonlinear Approximation with Finite Terms

This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm Gm^P（., Ψ）. This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another Mgorithm introduced by Birge and Massart.     

THE RELATIONSHIP BETWEEN THE SPARSE SYMMETRIC BROYDEN METHOD AND THE M-TIME SECANT-LIKE MULTI-PROJECTION METHOD

In this paper, we discuss the relationship between the sparse symmetric Broyden （SPSB） method [1, 2] and m-time secant-like multi-projection （SMP） method [3] and prove that when m goes to infinity, the SMP method is corresponding to the SPSB method.     

Precise rates in the law of the logarithm for the moment convergence in Hilbert spaces

Let （X, Xn; n ≥1） be a sequence of i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with covariance operator ∑. Set Sn = X1 ＋ X2 ＋ ... ＋ Xn, n≥ 1. We prove that, for b 〉 -1,
lim ε→0 ε^2（b＋1） ∞ ∑n=1 （logn）^b/n^3/2 E{｜｜Sn｜｜-σε√nlogn}=σ^-2（b＋1）/（2b＋3）（b＋1） B｜｜Y｜^2b＋3
holds if EX=0,and E｜｜X｜｜^2（log｜｜x｜｜）^3bv（b＋4）〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑.