摘要
本文用分布(广义函数)的概念导出了刻画带内点约束的变分问题的解的分布欧拉方程,说明在这类问题中拉格朗日乘子法仍然是有效的。此外,利用基本解给出了分布欧拉方程的解的表示。进而给出了一元和多元广义变分样条函数的表示的一般方法。
A system of distributional Euler＇s equations, characterizing the solutions of variational problems with interior constraints, is derived by using concepts of distributions（generalized functions）, i.e. Lagrange multiplier technique still plays a role in such kind of problems. Further, a representation of the solutions of DEE is given by taking use of the fundamental solutions, and therefore a general method for representation of univariate, and multivariate generalized variational spline function is provided.
出处
《计算数学》
CSCD
北大核心
2006年第3期225-236,共12页
Mathematica Numerica Sinica
关键词
分布欧拉方程
广义变分样条
变分法
Distributional Euler＇s equations, Generalized variational splines,Calculus of variations
