【摘要】 <正>1引言记P_n为次数不超过n的一元多项式函数类,约定零多项式的次数为-∞,即deg（0）=-∞;记R_（m,n）为分子属于P_m,分母属于P_n\{0}的一元有理函数类。在[1-5]的基础上,文[6]引进了有理插值问题的（m/n）_f方程组,其为经典（m/n）_f方程组的一种等价变换,由于变换之后,使得参数之间地位相同,并且在个数上也与空间自由度一致,因此成为分析有理插值的一个有力工具,文[7]利用（m/n）_f方程组,讨论了有理插值的基本特征,给出并证明了关于基本特征的基本关系定理,文[8]则在此基础上解决了有理插值的适定性问题。更多还原

【Abstract】 This paper analyses the（m/n）_f system of equations in the rational interpolating problem,obtains the properties and actions of the system.Using the （m/n）_f system of equations,it provides the definitions of the essential characteristics of the rational interpolating problem,discusses the fundamental structure of the（m,n）_f,c-interpolant,and gives a direct proof of the fundamental relation theorem of the essential characteristics.At last,it introduces the elementary solution, obtains the relations between general solution and elementary solution,and constructively reveals the fundamental structure of the general solution of the（m/n）_f system of equations.更多还原