An Adaptive Algorithm For Knots Of Cubic B-Spline In Data Fitting

As efficient in data fitting, spline has developed rapidly and been used extensively.In this paper, we consider least squares adaptive approach to random data implemented by cubic B-spline, which is a problem concentrating on the construction of a cubic B-spline, whose err sum of squares is less than a given precision. Through choosing the knots randomly, we get the vector of knots that enables the B-spline up to the given precision. We also make the number and the distribution of knots optimized in the sense of probability.The paper is structured as follows. The following section will introduce the research background, the basic method and tool used in data fitting, and the focus of this paper-least squares splines with free knots. Then we shall present the basic of B-spline as preliminary. Next, least squares splines with fixed knots and free knots will be interpreted respectively with a great emphasis on a algorithm called alternating iteration. Next we shall give an adaptive algorithm for knots of cubic B-spline in data fitting using stochastic method. We shall explain the feasibility of our method theoretically and present an algorithm for choosing the knots randomly, transforming the problem to linear least squares. Also the optimization of knots on the aspects of number and distribution will be given in this section. Finally, we shall examine some test examples and draw conclusions.