Two hierarchies of spline interpolations. Practical algorithms for multivariate higher order splines
نویسنده
چکیده
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular, rectangular grids, but an approach to other types of grids is also discussed.
منابع مشابه
A Comparison of Thin Plate and Spherical Splines with Multiple Regression
Thin plate and spherical splines are nonparametric methods suitable for spatial data analysis. Thin plate splines acquire efficient practical and high precision solutions in spatial interpolations. Two components in the model fitting is considered: spatial deviations of data and the model roughness. On the other hand, in parametric regression, the relationship between explanatory and response v...
متن کاملStudy of Evolutionary and Swarm Intelligent Techniques for Soccer Robot Path Planning
Finding an optimal path for a robot in a soccer field involves different parameters such as the positions of the robot, positions of the obstacles, etc. Due to simplicity and smoothness of Ferguson Spline, it has been employed for path planning between arbitrary points on the field in many research teams. In order to optimize the parameters of Ferguson Spline some evolutionary or intelligent al...
متن کاملInterpolation of fuzzy data by using flat end fuzzy splines
In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
متن کاملA Higher Order B-Splines 1-D Finite Element Analysis of Lossy Dispersive Inhomogeneous Planar Layers
In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and...
متن کاملMaterial-point method analysis of bending in elastic beams
The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consisten...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/0905.3564 شماره
صفحات -
تاریخ انتشار 2009