利用莫尔条纹的准正弦特性的三维轮廓术

分析了两个矩形光栅迭合产生的莫尔条纹的光强分布特性，通过选择适当的光栅参数，可得到一个近似的正弦分划板，并把它用于三维面形测量中，实验结果表明，这种方法简单，易于自动处理，有广泛的实用价值。     

水准折光及双波长激光效应

本文从“同温度层不完全平行于地面,且在变化”的“任意分层”假设出发,导出了水准折光修正公式,并利用光的色散效应在10~(-6)的精度要求下,求得r=r_T=h_1/h_2=(n_(01)-1)/(n_(02)-1)=常数最后指出,研制双波长激光水准仪的必要性和可能性,并提出了研制此种仪器的技术参数.     

有红利美式看跌期权定价的Crank-Nicolson有限差分法

本文基于B-S微分方程,采用Crank-Nicolson差分格式(简称C-N差分格式)求解支付固定红利的美式看跌期权价值,给出实证分析,并对C-N差分格式和隐含的差分格式进行了比较.结果表明,用C-N差分格式可以得到更加精确、有效的数值解.     

Nonparametric tests for bounds on the derivative of a regression function

We consider two tests of the null hypothesis that the k-th derivative of a regression function is uniformly bounded by a specified constant. These tests can be used to study the shape of the regression function. For instance, we can test for convexity of the regression function by setting k=2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic distribution and efficacies of these tests are computed and simulation results presented.Research supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0007969.Research supported by National Science Foundation Grant DMS-9306738.     

Sharp van der Corput estimates and minimal divided differences

We find the sharp constant in a sublevel set estimate which arises in connection with van der Corput's lemma. In order to do this, we find the nodes that minimise divided differences. We go on to find the sharp constant in the first instance of the van der Corput lemma. With these bounds we improve the constant in the general van der Corput lemma, so that it is asymptotically sharp.

     

Convergence analysis of a family of Steffensen-type methods for generalized equations

A class of Steffensen-type algorithms for solving generalized equations on Banach spaces is proposed. Using well-known fixed point theorem for set-valued maps [A.L. Dontchev, W.W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) 481-489] and some conditions on the first-order divided difference, we provide a local convergence analysis. We also study the perturbed problem and we present a new regula-falsi-type method for set-valued mapping. This study follows the works on the Secant-type method presented in [S. Hilout, A uniparametric Secant-type methods for nonsmooth generalized equations, Positivity (2007), submitted for publication; S. Hilout, A. Piétrus, A semilocal convergence of a Secant-type method for solving generalized equations, Positivity 10 (2006) 673-700] and extends the results related to the resolution of nonlinear equations [M.A. Hernández, M.J. Rubio, The Secant method and divided differences Hölder continuous, Appl. Math. Comput. 124 (2001) 139-149; M.A. Hernández, M.J. Rubio, Semilocal convergence of the Secant method under mild convergence conditions of differentiability, Comput. Math. Appl. 44 (2002) 277-285; M.A. Hernández, M.J. Rubio, ω-Conditioned divided differences to solve nonlinear equations, in: Monogr. Semin. Mat. García Galdeano, vol. 27, 2003, pp. 323-330; M.A. Hernández, M.J. Rubio, A modification of Newton's method for nondifferentiable equations, J. Comput. Appl. Math. 164/165 (2004) 323-330].     

Characterization of polynomials and divided difference

For distinct points x₁,x₂,…,x_n in ℛ (the reals), letϕ[x₁, x₂,…,x_n] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x₁,x₂,…,x_n] =g(x₁,+ x₂ + … + x_n) for distinct x₁,x₂,…, x_n in ℛ without any regularity assumptions on the unknown functions.     

Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

基于切比雪夫节点的一类带显式系数的广义高斯求积公式(英文)

The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind,and those of the（n-1）st Chebyshev polynomial of the second kind.Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences,which was proposed in[14].