圓柱曲面上的Lagrange插值
發(fā)布時(shí)間：2018-09-18 08:15
【摘要】：多元多項(xiàng)式插值,特別是多元Lagrange插值,一直是計(jì)算數(shù)學(xué)領(lǐng)域重要的研究課題之一.圓柱曲面是一類重要的二次代數(shù)曲面,在工業(yè)設(shè)計(jì)及數(shù)學(xué)物理方程等領(lǐng)域有重要應(yīng)用.本文主要將疊加插值法和因式分解法應(yīng)用于沿圓柱曲面Lagrange插值問題的適定性研究.首先,在引入有關(guān)的基本概念的基礎(chǔ)上,證明了沿柱面疊加插值法構(gòu)造適定結(jié)點(diǎn)組的一般性結(jié)果,包括構(gòu)造Rn(3)的插值適定結(jié)點(diǎn)組的添加柱面法,構(gòu)造沿柱面的n+k次插值適定結(jié)點(diǎn)組的添加柱面曲線組法,以及構(gòu)成沿柱面(或柱面曲線)的n次插值適定結(jié)點(diǎn)組的充分必要條件.然后,針對幾種具體的代數(shù)曲線,利用疊加插值法和因式分解法兩種方法給出了構(gòu)造沿柱面的三元n次插值適定結(jié)點(diǎn)組的添加母線法、添加二次不可約曲線法和添加雙圓周等方法,并針對添加圓周法給出了具體的插值格式和例子.
[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.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O241.3
本文編號：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.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O241.3
【參考文獻(xiàn)】
相關(guān)博士學(xué)位論文 前1條
1 張明;代數(shù)流形上的Lagrange插值和Hermite插值[D];吉林大學(xué);2009年
，本文編號：2247307
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