High Degree Polynomial Interpolation in Newton Form

1991 ◽  
Vol 12 (3) ◽  
pp. 648-667 ◽  
Author(s):  
Hillel Tal-Ezer
Keyword(s):  
Polynomial Interpolation ◽  
Degree Polynomial ◽  
High Degree

scholarly journals Efficient high degree polynomial root finding using GPU

2017 ◽  
Vol 18 ◽  
pp. 46-56 ◽  
Author(s):  
Kahina Ghidouche ◽  
Abderrahmane Sider ◽  
Raphaël Couturier ◽  
Christophe Guyeux
Keyword(s):  
Degree Polynomial ◽  
Root Finding ◽  
High Degree ◽  
Polynomial Root Finding

The Representation of Ship Hulls by Conformal Mapping Functions: Fractional Maps

1983 ◽  
Vol 27 (03) ◽  
pp. 158-159
Author(s):  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Longitudinal Direction ◽  
Interpolation Scheme ◽  
Mapping Functions ◽  
Ship Hulls ◽  
The Cross ◽  
High Degree

The method for analytically representing ship hulls by conformal mapping functions of the cross sections and lengthwise polynomial interpolation of the mappings, which was developed by von Kerczek and Tuck [1], has found useful applications to ship hydrodynamics (see references [2] and [3]) as well as ship design [4]. In both such applications, however, there have been two major criticisms of this type of representation of the underwater portion of the ship hull. The first criticism concerned the occurrence of undesirable waviness in the longitudinal direction of the cross sections of the ship. This waviness is due to fitting high-degree polynomials to very slowly varying data. This defect of the surface representation can be removed easily by abandoning the polynomial interpolation and substituting some form of spline interpolation. It has been found that interpolation by simple Hermite cubic splines works very well. Such modifications of the lengthwise interpolation scheme are well known and need no elaboration.

A subdivision algorithm to reason on high-degree polynomial constraints over finite domains

2019 ◽  
Vol 87 (4) ◽  
pp. 343-360
Author(s):  
Federico Bergenti ◽  
Stefania Monica
Keyword(s):  
Degree Polynomial ◽  
Subdivision Algorithm ◽  
High Degree ◽  
Finite Domains ◽  
Polynomial Constraints

A non-oscillatory and conservative semi-Lagrangian scheme with fourth-degree polynomial interpolation for solving the Vlasov equation

2012 ◽  
Vol 183 (5) ◽  
pp. 1094-1100 ◽  
Author(s):  
Takayuki Umeda ◽  
Yasuhiro Nariyuki ◽  
Daichi Kariya
Keyword(s):  
Vlasov Equation ◽  
Polynomial Interpolation ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Lagrangian Scheme

scholarly journals Finding the Zeros of a High-Degree Polynomial Sequence

2021 ◽  
Vol 29 (2) ◽  
pp. 119
Author(s):  
Vladimir L. Borsch ◽  
Peter I. Kogut
Keyword(s):  
Degree Polynomial ◽  
Polynomial Sequence ◽  
High Degree

Polynomial Surface Representation of Arbitrary Ship Forms

1960 ◽  
Vol 4 (02) ◽  
pp. 12-21 ◽  
Author(s):  
J. E. Kerwin
Keyword(s):  
Degree Polynomial ◽  
Surface Representation ◽  
Numerical Examples ◽  
Hydrodynamic Calculations ◽  
Analytic Expression ◽  
Hull Forms ◽  
High Degree ◽  
Polynomial Surface

This paper is concerned with the approximation of an arbitrary hull shape by an analytic expression to be used primarily for hydrodynamic calculations. A method is described which permits high-degree polynomial surface equations to be used as approximations of a wide variety of hull shapes. Numerical examples obtained with an IBM 704 computer show that the procedure produces hull forms which are sufficiently accurate for most hydrodynamic calculations.

scholarly journals Oblivious Sketching of High-Degree Polynomial Kernels

2020 ◽  
pp. 141-160 ◽  
Author(s):  
Thomas D. Ahle ◽  
Michael Kapralov ◽  
Jakob B. T. Knudsen ◽  
Rasmus Pagh ◽  
Ameya Velingker ◽  
...  
Keyword(s):  
Degree Polynomial ◽  
High Degree ◽  
Polynomial Kernels

scholarly journals Trajectory Planning of Robot Manipulator Based on RBF Neural Network

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1207
Author(s):  
Qisong Song ◽  
Shaobo Li ◽  
Qiang Bai ◽  
Jing Yang ◽  
Ansi Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Trajectory Planning ◽  
Polynomial Interpolation ◽  
Robot Manipulator ◽  
Rbf Neural Network ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Degree Of Freedom ◽  
Quintic Polynomial ◽  
High Degree

Robot manipulator trajectory planning is one of the core robot technologies, and the design of controllers can improve the trajectory accuracy of manipulators. However, most of the controllers designed at this stage have not been able to effectively solve the nonlinearity and uncertainty problems of the high degree of freedom manipulators. In order to overcome these problems and improve the trajectory performance of the high degree of freedom manipulators, a manipulator trajectory planning method based on a radial basis function (RBF) neural network is proposed in this work. Firstly, a 6-DOF robot experimental platform was designed and built. Secondly, the overall manipulator trajectory planning framework was designed, which included manipulator kinematics and dynamics and a quintic polynomial interpolation algorithm. Then, an adaptive robust controller based on an RBF neural network was designed to deal with the nonlinearity and uncertainty problems, and Lyapunov theory was used to ensure the stability of the manipulator control system and the convergence of the tracking error. Finally, to test the method, a simulation and experiment were carried out. The simulation results showed that the proposed method improved the response and tracking performance to a certain extent, reduced the adjustment time and chattering, and ensured the smooth operation of the manipulator in the course of trajectory planning. The experimental results verified the effectiveness and feasibility of the method proposed in this paper.

High-degree polynomial models for CT simulation

2012 ◽  
Vol 20 (4) ◽  
pp. 447-457
Author(s):  
Yingkang Hu ◽  
Jiehua Zhu
Keyword(s):  
Degree Polynomial ◽  
Ct Simulation ◽  
Polynomial Models ◽  
High Degree

scholarly journals Polynomial Interpolation of Normal Conditional Expectation

2019 ◽  
Vol 8 (3) ◽  
pp. 75
Author(s):  
Anis Rezgui
Keyword(s):  
Error Estimation ◽  
Conditional Expectation ◽  
Polynomial Function ◽  
Polynomial Interpolation ◽  
Random Variable ◽  
Standard Normal Distribution ◽  
Degree Polynomial ◽  
Reasonable Condition ◽  
Pointwise Error ◽  
Standard Normal

In this paper we are interested in approximating the conditional expectation of a given random variable X with respect to the standard normal distribution N(0, 1). Actually we have shown that the conditional expectation E(X|Z) could be interpolated by an N degree polynomial function of Z, φN(Z) where N is the number of observations recorded for the conditional expectation E(X|Z = z). A pointwise error estimation has been proved under reasonable condition on the random variable X.

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