摘要
构造具有可列个型值点和一定光滑性要求的插值函数，是解决一元函数极限与二元函数极限之关系的关键．首先讨论了具有可列个型值点的插值函数的光滑性问题；然后利用分析的方法构造了具有可列个型值点且具有一定光滑性要求的插值分段多项式．结论是无穷数列｛ｘｎ｝单调上升且收敛于ｘ０，｛ｙｎ｝是任给的无穷数列，则可以构造以（ｘｎ，ｙｎ）为型值点的五阶光滑的插值分段多项多（ｎ＝１，２，３，…）；
To solving the relationship between the limit of function of a variable and function of double variables, the key consists in constructing the smooth interpolating function with countable special value points. First, the smooth properties of interpolating function with countable special value points is discussed; then, the interpolating piecewise polynomial with countable special value points is constructed by the use of analysis mathod. The coclusion is: if an increasing sequence {xn}, xn→x0(n→∞), and for any sequence {yn}, then the interpolating piecewise polynomial with special value points (xn, yn) can be constructed (n=1,2,3,…). Further more, using the conclusion, the relationship between the limit of function of a variable and function of double variables is given.
出处
《湖北大学学报（自然科学版）》
CAS
1997年第4期317-322,共6页
Journal of Hubei University：Natural Science
关键词
型值点
插值函数
插值分段多项式
光滑
Special value points
Interpolating function
Interpolating piecewise polynomial
Smooth
