Optimal Interpolation Algorithm Research Based on Quasi-Hermite Space Curve

2011 ◽  
Vol 317-319 ◽  
pp. 215-221
Author(s):  
Chang Chun Liang ◽  
Liu Qun Fan ◽  
Dang Jin Qi ◽  
Gang Yi ◽  
Zhuang Miao
Keyword(s):  
Hermite Polynomial ◽  
Polynomial Interpolation ◽  
Recursive Algorithm ◽  
Optimal Interpolation ◽  
Taylor Formula ◽  
Interpolation Algorithm ◽  
Parametric Curve ◽  
Interpolation Accuracy ◽  
The Stability ◽  
Accuracy Of Approximation

According to the principle of parametric curve paths CNC interpolating, a real-time interpolation algorithm based on algebraic index of the micro-segment spline is presented. It’s used to solve the problems of Hermite polynomial interpolation algorithm, which are commonly slow recursive algorithm, poor accuracy of approximation and the limitations of constant parameters increment interpolation. And the constant interpolation is achieved by fitting a first-order Taylor Formula. Simulation results show that the algorithm shortens the interpolation time and also improve the interpolation accuracy; meanwhile, it maintains the stability of the feed rate.

scholarly journals Profiled Horn Antenna with Wideband Capability Targeting Sub-THz Applications

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 412
Author(s):  
Jay Gupta ◽  
Dhaval Pujara ◽  
Jorge Teniente
Keyword(s):  
Hermite Polynomial ◽  
Polynomial Interpolation ◽  
Horn Antenna ◽  
Submillimeter Wavelengths ◽  
Thz Applications ◽  
Millimeter And Submillimeter Wavelengths ◽  
Better Than

This paper proposes a wideband profiled horn antenna designed using the piecewise biarc Hermite polynomial interpolation and validated experimentally at 55 GHz. The proposed design proves S11 and directivity better than −22 dB and 25.5 dB across the entire band and only needs 3 node points if compared with the well-known spline profiled horn antenna. Our design makes use of an increasing radius and hence does not present non-accessible regions from the aperture, allowing its fabrication with electro erosion techniques especially suitable for millimeter and submillimeter wavelengths.

Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

2013 ◽  
Vol 318 ◽  
pp. 100-107
Author(s):  
Zhen Shen ◽  
Biao Wang ◽  
Hui Yang ◽  
Yun Zheng
Keyword(s):  
Data Exchange ◽  
Shape Function ◽  
Interpolation Method ◽  
Matching Condition ◽  
Optimal Interpolation ◽  
Complex Interpolation ◽  
Interpolation Function ◽  
Interpolation Methods ◽  
Interpolation Accuracy ◽  
Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

scholarly journals A New Approach to Newton-Type Polynomial Interpolation with Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Le Zou ◽  
Liangtu Song ◽  
Xiaofeng Wang ◽  
Thomas Weise ◽  
Yanping Chen ◽  
...  
Keyword(s):  
Polynomial Interpolation ◽  
Information Matrix ◽  
Divided Differences ◽  
Mathematical Representation ◽  
Interpolation Algorithm ◽  
New Approach ◽  
Multiple Parameters ◽  
Parameter Values ◽  
The Given ◽  
Interpolation Functions

Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.

Derived Nodes Approach for Improving Accuracy of Machining Stability Prediction

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Le Cao ◽  
Xiao-Ming Zhang ◽  
Tao Huang ◽  
Han Ding
Keyword(s):  
State Space ◽  
Polynomial Interpolation ◽  
Recursive Estimation ◽  
Machining Process ◽  
Stability Prediction ◽  
State Variables ◽  
Piecewise Polynomials ◽  
Discrete Equations ◽  
Runge Phenomenon ◽  
The Stability

Machining process dynamics can be described by state-space delayed differential equations (DDEs). To numerically predict the process stability, diverse piecewise polynomial interpolation is often utilized to discretize the continuous DDEs into a set of linear discrete equations. The accuracy of discrete approximation of the DDEs generally depends on how to deal with the piecewise polynomials. However, the improvement of the stability prediction accuracy cannot be always guaranteed by higher-order polynomials due to the Runge phenomenon. In this study, the piecewise polynomials with derivative-continuous at joint nodes are taken into consideration. We develop a recursive estimation of derived nodes for interpolation approximation of the state variables, so as to improve the discretization accuracy of the DDEs. Two different temporal discretization methods, i.e., second-order full-discretization and state-space temporal finite methods, are taken as demonstrations to illustrate the effectiveness of applying the proposed approach for accuracy improvement. Numerical simulations prove that the proposed approach brings a great improvement on the accuracy of the stability lobes, as well as the rate of convergence, compared to the previous recorded ones with the same order of interpolation polynomials.

scholarly journals Adaptation of a fast optimal interpolation algorithm to the mapping of oceanographic data

1997 ◽  
Vol 102 (C5) ◽  
pp. 10573-10584 ◽  
Author(s):  
Dimitris Menemenlis ◽  
Paul Fieguth ◽  
Carl Wunsch ◽  
Alan Willsky
Keyword(s):  
Optimal Interpolation ◽  
Interpolation Algorithm ◽  
Oceanographic Data

scholarly journals The Performance Improvement of the Low-Cost Ultrasonic Range Finder (HC-SR04) Using Newton’s Polynomial Interpolation Algorithm

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Gutama Indra Gandha ◽  
Dedi Nurcipto
Keyword(s):  
Polynomial Interpolation ◽  
Low Cost ◽  
General Purpose ◽  
Computer Applications ◽  
Range Finder ◽  
Interpolation Algorithm ◽  
Measuring Process ◽  
Underwater Environment ◽  
Industrial Grade ◽  
Accuracy Level

The ultrasonic range finder sensors are widely used sensor in many applications such as computer applications, general purpose applications, medical applications, automotive applications and industrial grade applications. The ultrasonic range finder sensor has many advantages. The advantages are easy to use, fast in measuring process, non-contact measurement and suitable for air and underwater environment. However, the ultrasonic range finder has deviation especially for low-cost sensor. It affects the accuracy level of the measurement result that performed by its sensor directly. The HC-SR04 categorized as a low-cost ultrasonic range finder sensor. This sensor has significant error level. The improvement of the accuracy level of this low-cost ultrasonic sensor is expected to this research. The Newton’s polynomial interpolation algorithm has been used in this research to reduce the error during the measurement process. The implementation of Newton’s polynomial interpolation has succeeded to improve the sensor accuracy. The MSE level of 29,96 is obtained without the Newton’s Polynomial Interpolation implementation. The implementation of the Newton’s Polynomial Interpolation algorithm has succeeded to increase the accuracy level of the sensor by 55,54%. It has been proofed by the decrease of MSE level by 13,32.

scholarly journals A New Radial Basis Function Approach Based on Hermite Expansion with Respect to the Shape Parameter

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 979
Author(s):  
Saleh A. Bawazeer ◽  
Saleh S. Baakeem ◽  
Abdulmajeed A. Mohamad
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Hermite Polynomial ◽  
Shape Parameter ◽  
Hermite Expansion ◽  
Node Distribution ◽  
Radial Basis ◽  
The Stability ◽  
Stability And Accuracy ◽  
Truncation Order

Owing to its high accuracy, the radial basis function (RBF) is gaining popularity in function interpolation and for solving partial differential equations (PDEs). The implementation of RBF methods is independent of the locations of the points and the dimensionality of the problems. However, the stability and accuracy of RBF methods depend significantly on the shape parameter, which is mainly affected by the basis function and the node distribution. If the shape parameter has a small value, then the RBF becomes accurate but unstable. Several approaches have been proposed in the literature to overcome the instability issue. Changing or expanding the radial basis function is one of the most commonly used approaches because it addresses the stability problem directly. However, the main issue with most of those approaches is that they require the optimization of additional parameters, such as the truncation order of the expansion, to obtain the desired accuracy. In this work, the Hermite polynomial is used to expand the RBF with respect to the shape parameter to determine a stable basis, even when the shape parameter approaches zero, and the approach does not require the optimization of any parameters. Furthermore, the Hermite polynomial properties enable the RBF to be evaluated stably even when the shape parameter equals zero. The proposed approach was benchmarked to test its reliability, and the obtained results indicate that the accuracy is independent of or weakly dependent on the shape parameter. However, the convergence depends on the order of the truncation of the expansion. Additionally, it is observed that the new approach improves accuracy and yields the accurate interpolation, derivative approximation, and PDE solution.

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