带参数的多结点样条

Many-Knot Spline with A Parameter

多结点样条函数是在通常样条函数中引入更多的附加结点 ,其优越性表现在使插值过程无须求解任何方程组 ,而且有局部性 对多结点样条函数做进一步研究 ,构造了一类带参数的多结点样条基本函数 该类函数不仅保持了一般多结点样条函数的优点 ,而且由于参数的引进 ,使得基数型的插值公式可形成一族 ,可以根据实际问题的需要在函数 (曲线 )族中作出最优选择 文中研究的带参数的多结点样条函数 ,除了能用于表达平滑的数据及几何造型之外 ,尤其能适应波动较大、频率较高的数据拟合问题 。

The many knot spline functions introduce more knots than those of traditional spline functions It has the advantages of no need to solve any system of equations for interpolation and being localized Making a step further, a new class of many knot spline function with a parameter is constructed This class not only preserves the advantages of the original spline functions, but also gives rise to a class of cardinal type interpolation formulas owing to the additional parameter Therefore, one can make the best choice to meet the needs of practical problems The many knot spline function with a parameter can be used to fit smooth data and fulfil geometric design, it is also especially suitable for fitting data with fairly big fluctuation of comparatively high frequency This is very helpful for solving the problems of signal processing and making irregular geometric design