圆柱曲面上的Lagrange插值
发布时间：2018-09-18 08:15
【摘要】：多元多项式插值,特别是多元Lagrange插值,一直是计算数学领域重要的研究课题之一.圆柱曲面是一类重要的二次代数曲面,在工业设计及数学物理方程等领域有重要应用.本文主要将叠加插值法和因式分解法应用于沿圆柱曲面Lagrange插值问题的适定性研究.首先,在引入有关的基本概念的基础上,证明了沿柱面叠加插值法构造适定结点组的一般性结果,包括构造Rn(3)的插值适定结点组的添加柱面法,构造沿柱面的n+k次插值适定结点组的添加柱面曲线组法,以及构成沿柱面(或柱面曲线)的n次插值适定结点组的充分必要条件.然后,针对几种具体的代数曲线,利用叠加插值法和因式分解法两种方法给出了构造沿柱面的三元n次插值适定结点组的添加母线法、添加二次不可约曲线法和添加双圆周等方法,并针对添加圆周法给出了具体的插值格式和例子.
[Abstract]:Multivariate polynomial interpolation, especially multivariate Lagrange interpolation, has been one of the most important research topics in computational mathematics. Cylindrical surfaces are a class of important quadratic algebraic surfaces, which have important applications in the fields of industrial design and mathematical and physical equations. In this paper, the superposition interpolation method and the factorization method are applied to the Lagrange interpolation problem along the cylindrical surface. First of all, on the basis of introducing some basic concepts, we prove the general results of constructing a set of suitable nodes by superposition interpolation along the cylinder, including the addition of cylinder method for constructing Rn (3). In this paper, we construct the method of adding cylindrical curve for n-k-degree interpolating suitable node group along cylinder, and the necessary and sufficient condition for constructing n-degree interpolating suitable node system along cylinder (or cylindrical curve). Then, in view of several specific algebraic curves, the addition generatrix method of constructing 3-dimensional n-degree interpolation suitable node group along the cylinder is given by means of superposition interpolation method and factorization method. The methods of adding quadratic irreducible curve and adding double circle are added, and the interpolation scheme and examples are given for adding circle method.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.3
本文编号：2247307
[Abstract]:Multivariate polynomial interpolation, especially multivariate Lagrange interpolation, has been one of the most important research topics in computational mathematics. Cylindrical surfaces are a class of important quadratic algebraic surfaces, which have important applications in the fields of industrial design and mathematical and physical equations. In this paper, the superposition interpolation method and the factorization method are applied to the Lagrange interpolation problem along the cylindrical surface. First of all, on the basis of introducing some basic concepts, we prove the general results of constructing a set of suitable nodes by superposition interpolation along the cylinder, including the addition of cylinder method for constructing Rn (3). In this paper, we construct the method of adding cylindrical curve for n-k-degree interpolating suitable node group along cylinder, and the necessary and sufficient condition for constructing n-degree interpolating suitable node system along cylinder (or cylindrical curve). Then, in view of several specific algebraic curves, the addition generatrix method of constructing 3-dimensional n-degree interpolation suitable node group along the cylinder is given by means of superposition interpolation method and factorization method. The methods of adding quadratic irreducible curve and adding double circle are added, and the interpolation scheme and examples are given for adding circle method.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.3
【参考文献】
相关博士学位论文 前1条
1 张明;代数流形上的Lagrange插值和Hermite插值[D];吉林大学;2009年
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