基于函数值的四次有理插值样条及其应用

Rational quartic interpolating spline based on function values and its application

构造了一种新的仅基于函数值的C1连续四次有理插值样条,其分子为四次多项式、分母是二次多项式.由于这种新的四次有理插值样条中含有3个参数和一个调节参数,因而在给定插值数据不变的前提下,能通过改变插值函数中参数与调节参数来更灵活地对插值曲线的局部进行修改,给约束控制带来了方便.对该种插值曲线的形状控制问题进行了研究,给出了将其约束于给定的折线、二次曲线之上、之下或之间的充分条件,改进和推广了一些相关结论.最后给出了数值例子。

A new rational quartic interpolating spline based on function values with quadratic denominators is constructed. The new interpolating function contains three parameters and a adjustable parameter. The interpolating function can be used for the modification of local curves by selecting suitable parameters under the condition that the interpolating data are not changed. The sufficient conditions for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves are derived. Some related results reported in the literature are extended or improved. An example is given.