PSO节点寻优的样条逼近微分

样条节点分布对逼近精度的影响很大,样条节点寻优模型的雅可比矩阵求解复杂。利用经典参数的PSO（粒子群算法）解算样条最优节点分布模型,以逼近残差的平方和为目标函数,每步对节点序列排序后再计算目标函数,可以提高样条逼近精度,为样条节点寻优提供了一种较好的实现方法。仿真计算表明,在一定的节点个数情况下,PSO节点寻优的逼近效果比Carl de Boor的NEWNOT程序中的方法要好。

Spline Approximation Differential with PSO Knot Placement Majorization

Spline knot placement has a big impact on approximation accuracy and Jacobi matrix in knot placement optimization is difficult to get.This paper uses off-the-shelf PSO to search the optimization knot placement.The fitness function is approximation residual sum of squares and is calculated each step after sorting the sequence of knots.This brings more accurate approximation and gives a better method for knot placement optimization.Simulation and experiments show that PSO knot placement enables more accurate approximation than knot placement calculated in Carl de Boor’s NEWNOT program with certain knot number.