带边界条件样条函数空间S21,1(△mn(2))上的Lagrange插值

Lagrange Interpolation of Bivariate Quadratic Splines S21,1(△mn(2)) with Boundary Conditions

关键词:  非均匀(Ⅱ)型三角剖分  二元二次样条  边界条件  支集中心插值

Key words:  non-uniform type-Ⅱ triangulation  bivariate quadratic splines  boundary conditions  interpolation to the center of the support

摘要:

讨论非均匀(Ⅱ)型三角剖分△_mn⁽²⁾上二元二次样条空间的带边界条件子空间S₂^1,1(△_mn⁽²⁾)上的一类所谓支集中心型的Lagrange插值。运用矩阵方向图技术,证明当△_mn⁽²⁾满足所谓非降比剖分条件时相应的插值问题适定,在此条件下,得到插值函数的Lagrange型表示。

Abstract:

A kind of Lagrange interpolation by bivariate quadratic splines with boundary conditions over non-uniform type-Ⅱ triangulation, called the interpolation to the center of the support of splines, is discussed.By using the oriented graphic technique of matrix, the existence and the uniqueness of the interpolation are obtained for a special triangulation. Furthermore, the representation of the interpolation function is given.