有理插值(m/n)_f方程组的性质与作用  

THE PROPERTIES AND ACTIONS OF THE (m/n)_f SYSTEM OF EQUATIONS IN THE RATIONAL INTERPOLATING PROBLEM

作　　者：穆罕默德[1] 朱本喜[1] 王晓辉[2] 盛中平[2] 

机构地区：[1]吉林大学数学学院,长春130012 [2]东北师范大学数学系,长春130024

出　　处：《高等学校计算数学学报》2009年第2期148-155,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(10571102)

摘　　要：记Pn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Rm,n为分子属于Pm，分母属于Pn/{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，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.

关 键 词：有理插值问题 方程组 一元多项式 性质 等价变换 函数类 自由度 分子 

分 类 号：O241.3[理学—计算数学] O241.6[理学—数学]