Bounds of Interpolation Error for Arbitrary Narrow Quadrilateral Quasi-Wilson Element

Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).

Calculation of Space NURBS Curve Interpolation Error

Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.

ERROR ESTIMATION OF INTERPOLATION ON PORE STRUCTURE ANALYSIS

In this paper we computed the data of pore structure with Lagrange interpolation method, analyzed the convergence of the method and deduced the corresponding error estimation formula.

THE CRUCIAL CONSTANTS IN THE EXPONENTIAL-TYPE ERROR ESTIMATES FOR GAUSSIAN INTERPOLATION

It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.

Generalized Inverse Vector Valued Osculatory Rational Interpolation and Its Error Formula

In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t'ormalism of Graves-Moms (1983). In the computation of the osculatory continued h.actions, the three term recurrence relation is avoided and a new coefficient algorithm is introduced, which is the characteristic of recursive operation. Some examples are given to illustrate its effectiveness. A sutficient condition for cxistence is established. Some interpolating properties including uniqueness are discussed. In the end, all exact interpolating error formula is obtained.

On the Average Errors of Multivariate Lagrange Interpolation

In this paper, we discuss the average errors of multivariate Lagrange interpolation based on the Chebyshev nodes of the first kind. The average errors of the interpolation sequence are determined on the multivariate Wiener space.

A MODIFIED EDGE-ORIENTED SPATIAL INTERPOLATION ALGORITHM FOR CONSECUTIVE BLOCKS ERROR CONCEALMENT

This paper proposes a low-complexity spatial-domain Error Concealment (EC) algorithm for recovering consecutive blocks error in still images or Intra-coded (I) frames of video sequences. The proposed algorithm works with the following steps. Firstly the Sobel operator is performed on the top and bottom adjacent pixels to detect the most likely edge direction of current block area. After that one-Dimensional (1D) matching is used on the available block boundaries. Displacement between edge direction candidate and most likely edge direction is taken into consideration as an important factor to improve stability of 1D boundary matching. Then the corrupted pixels are recovered by linear weighting interpolation along the estimated edge direction. Finally the interpolated values are merged to get last recovered picture. Simulation results demonstrate that the proposed algorithms obtain good subjective quality and higher Peak Signal-to-Noise Ratio (PSNR) than the methods in literatures for most images.

ERROR BOUNDS IN PERIODIC QUARTIC SPLINE INTERPOLATION

In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).

Anisotropic Interpolation Error Estimates of a Nonconforming Element

The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

ON THE ERROR OF QUADRATURE FORMULAE FOR CAUCHY PRINCIPAL VALUE INTEGRALS BASED ON PIECEWISE INTERPOLATION

We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTION(Ⅱ)

Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.

ON NEWMAN-TYPE RATIONAL INTERPOLATION TO |x| AT THE CHEBYSHEV NODES OF THE SECOND KIND

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）

Study on Control Algorithm for Continuous Segments Trajectory Interpolation

In CNC machining,the complexity of the part contour causes a series of problems including the repeated start-stop of the motor,low machining efficiency,and poor machining quality.To relieve those problems,a new interpolation algorithm was put forward to realize the interpolation control of continuous sections trajectory.The relevant error analysis of the algorithm was also studied.The feasibility of the algorithm was proved by machining experiment using a laser machine to carve the interpola- tion trajectory in the CNC system GT100.This algorithm effectively improved the machining efficiency and the contour quality.

A Parametric Study of Mesh Free Interpolation Based Recovery Techniques in Finite Element Elastic Analysis

The paper presents a parametric study on interpolation techniques based postprocessed error estimation in finite element elastic analysis by varying important parameters of recovery,interpolation scheme and type of patch construction.The quality of error estimation with recovery parameters is compared in terms of local and global effectivity of error estimation,rate of error convergence,and adaptively refined meshes.A mesh free moving least square interpolation technique with proven reliability and effectivity is introduced for improving the recovery of finite element solution errors.The post-processed finite element solutions of elastic problems are presented for performance study under different parameters of recovery technique.The study concludes that recovery parameters of interpolation method have pronounced effect on the recovery of finite element solution error and analysis in adaptive environment.

Bivariate Blending Thiele-Werner's Osculatory Rational Interpolation

Both the expansive Newton's interpolating polynomial and the Thiele-Werner's in- terpolation are used to construct a kind of bivariate blending Thiele-Werner's oscula- tory rational interpolation.A recursive algorithm and its characteristic properties are given.An error estimation is obtained and a numerical example is illustrated.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF (1-x^2)cosnarccosx

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.

On Two Birkhoff-Type Interpolations with First- and Second-Order Derivative

In this paper, we consider two interpolations of Birkhoff-type with integer-order derivative. The Birkhoff interpolation is related with collocation method for the corresponding initial or boundary value problems of differential equations. The solvability of the interpolation problems is proved. For Gauss-type interpolating points, error of interpolation approximation is deduced. Also, we give efficient algorithms to implement the concerned interpolations.

A Type of C^2 Piecewise Rational Interpolation

A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.