A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL

In this paper, a new derivative free trust region method is developed basedon the conic interpolation model for the unconstrained optimization. The conic inter-polation model is built by means of the quadratic model function, the collinear scalingformula, quadratic approximation and interpolation. All the parameters in this model axedetermined by objective function interpolation condition. A new derivative free method isdeveloped based upon this model and the global convergence of this new method is provedwithout any information on gradient.     

基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

General Interpolation Formulae for Barycentric Blending Interpolation

General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.     

一种广义插值法

本文考虑一种广义插值问题，插值条件为小区间上的积分值，以弥补现有的插值方法在L2空间不再适用的不足，除了多项式插值外，还讨论了两种一次样条插值方法。     

General Structures of Block Based Interpolational Function

We construct general structures of one and two variable interpolation function,without depending on the existence of divided difference or inverse differences,and we also discuss the block based oscula...     

Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x _k) = a _k, D ^m T(x _k) = b _k, 0 k n – 1, where x _k = k/n is a nodal set, a _k and b _k are prescribed complex numbers, and m N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist.     

A Kind of Generalization of the Curve Type Node Configuration in R^S（S 〉 2）

A kind of generalization of the Curve Type Node Configuration is given in this paper,and it is called the generalized node configuration CTNCB in RS(S＞2).The related multivariate polynomial interpolation problem is discussed.It is proved that the CTNCB is an appropriate node configuration for the polynomial space PSn (S＞2).And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.     

Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.     

The real interpolation method on couples of intersections

Suppose that (X ₀, X ₁) is a Banach couple, X ₀ ∩ X ₁ is dense in X ₀ and X ₁, (X₀,X₁)_θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X ₀ ∩ X ₁), ψ ≠ 0, is a linear functional, N = Ker ψ, and N _i stands for N with the norm inherited from X _i (i = 0, 1). The following theorem is proved: the norms of the spaces (N₀,N₁)_θ,q and (X₀,X₁)_θ,q are equivalent on N if and only if θ ? (0, α) ∪ (β_∞, α₀ ∪ (β₀, α_∞) ∪ (β, 1), where α, β, α₀, β₀, α_∞, and β _∞ are the dilation indices of the function k(t)=K(t,ψ;X ₀ ^* ,X ₁ ^* ).     

THE ELLIPTIC TYPE NODE CONFIGURATION AND INTERPOLATION IN R~2

1.IlltroductionInthispaper,weusetheusualmultivariatenotationac=yi'w'B,iii=if ... j.(if,'',j.EZ )[l'a]andletPnbethe(bivariate)polynomialspaceofallreal(bivariate)polynomialsofdegreeatmostn.NowweintroducetheconceptoftheCurveTypeNodeConfiguration(CTNC):De…