三次B样条拟合的预处理渐进迭代逼近法OA

To improve the convergence efficiency of progressive-iterative approximation for large-scale data fitting,we introduce a class of Jacobi preconditioners and develop two preconditioned methods:preconditioned LSPIA and preconditioned PmLSPIA.The preconditioned LSPIA method employs Jacobi preconditioner to optimize control point updates,while the preconditioned PmLSPIA method further accelerates convergence by incorporating Polyak momentum.Due to the adoption of Jacobi-type preconditioner,the computational keeps remains minimal.Both theoretical analysis and experimental results demonstrate that the preconditioned methods outperform their non-preconditioned counterparts in terms of convergence rate and computational time,providing new insights for efficient geometric iterative methods.