一個多元函數的內插公式

本文介绍一个新型多元函数结构.它在一定条件下: 1)可根据一定的已知数值决定函数的其他近似值, 2)可作为构成经验公式的骨架.

A NEW THEORY OF INTERPOLATION FOR FUNCTION OF n VARIABLES

This paper describes the construction of a new function of n variables i,u,v,……,z,which becomes identical to the given function f(t,u,v,……, z) of n variables when (n-1) of the variables are each assigned their own specific values used in the construction of the function.In case of two variables, the surfaces of f(t, u) and coincide laong 4r sections at the values t_1,t_1′,t_2,t_2′,……,t_r, t_r′, u_1,u_1′,u_2,u_2′,……,u_r,u_r′. If both are ocntinuous and single-valued, actual examples indicate that the new function is a very close approximation of the original function f(t,u) within the region of cross-lines of coincidence.