Many-Knot Spline with A Parameter

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.