APPROXIMATION BY RATIONAL FUNCTIONS WITH POLYNOMIALS OF POSITIVE COEFFICIENTS AS THE DENOMINATORS

The present paper proves that if（x） ∈ C[0,1], changes its sign exactly l times at 0 〈 y1〈 y2 … 〈 y1 〈 1 in （0, 1）, then there exists a pn（x） ∈ Пn（＋）, such that ｜f（x）- p（x）/pn（x）｜≤ Cωφ（f,n^（-1/2））, where ρ（x） is defined by ρ（x）={^lПi=1（x-yi）,if f （x）≥0 for x ∈（y1,1）, {-^lПi=1（x-yi）,if f （x）〈0 for x ∈（y1,1）, which improves and generalizes the result of .

A REMARK ON THE COEFFICIENTS OF BOUNDED POLYNOMIALS

Let p(z)=akzk be such that |p(eip)|≤1 for R and |p(1)|=a[0,1].An inequality of Dewan and Cavil for the sum |av|+|au|,0≤u<v≤n is sharpened.Let p(z)=abzk be such that for R,

Accuracy and Efficiency: The Comparison of Different RPC Parameters Solving Methods

As a generalized sensor, the RPC model with its accuracy equally matches the physical sensor model. Moreover, the accurate positioning combining with the flexibility in application leads the RPC model to be the priority in photogrammetry processing. Generally, the RPC model is calculated through a control grid. Different RPC parameters solving methods and the operation efficiency all serve as variables in the accuracy of the model. In this paper, the ridge estimation iterative method, spectrum correction iteration, and conjugate gradient method are employed to solve RPC parameters;the accuracy and efficiency of three solving methods are analyzed and compared. The results show that ridge estimation iterative method and spectrum correction iteration have obvious advantages in accuracy. The ridge estimation iterative method has fewer iteration times and time con-sumption, and spectrum correction iteration has more stable precision.

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

The magnetohydrodynamics （MHD） Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An efficient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.

CHARACTERIZATION THEOREM OF GENERALIZED POLYNOMIAL OF BEST APPROXIMATION HAVING BOUNDED COEFFICIENTS

Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.

Two-stage Local Walsh Average Estimation of Generalized Varying Coefficient Models

In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.