有理插值问题不适定的根本原因  

THE ESSENTIAL REASON WHY THE RATIONAL INTERPOLATING PROBLEM IS ILL-POSED

作　　者：盛中平[1] 

机构地区：[1]东北师范大学数学系,长春130024

出　　处：《高等学校计算数学学报》2001年第3期227-236,共10页Numerical Mathematics A Journal of Chinese Universities

摘　　要：In this paper, we define several concepts about rational function, such as degree of binding and relative degree of binding, and reveal three phenomena that degree of binding or relative degree of binding can be equal to, less than or greater than degree of freedom in the rational interpolating problem. We introduce binding function of the rational interpolating problem, prove its existence and uniqueness, hence constructively grasp all the ill-posed or well posed cases of the rational interpolating problem.In this paper, we define several concepts about rational function, such as degree of binding and relative degree of binding, and reveal three phenomena that degree of binding or relative degree of binding can be equal to, less than or greater than degree of freedom in the rational interpolating problem. We introduce binding function of the rational interpolating problem, prove its existence and uniqueness, hence constructively grasp all the ill-posed or well posed cases of the rational interpolating problem.

关 键 词：有理插值 多项式函数类 自由度 束缚度 束缚函数 

分 类 号：O241.3[理学—计算数学]