浙江大学学报（理学版）2026，Vol.53Issue(2)：214-221,8.DOI:10.3785/1008-9497.25097
三次B样条拟合的预处理渐进迭代逼近法
Preconditioned progressive-iterative approximation for cubic B-spline fitting
摘要
Abstract
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.关键词
渐进迭代逼近/几何迭代法/B样条曲线曲面/最小二乘拟合/预处理Key words
progressive-iterative approximation/geometric iterative method/B-spline curve and surface/least-squares fitting/preconditioning分类
信息技术与安全科学引用本文复制引用
刘成志,吴念慈,李军成,胡丽娟..三次B样条拟合的预处理渐进迭代逼近法[J].浙江大学学报（理学版）,2026,53(2):214-221,8.基金项目
国家自然科学基金项目(12101225,12201651) （12101225,12201651）
湖南省自然科学基金项目(2023JJ50080) （2023JJ50080）
湖南省教育厅科学研究重点项目(24A0637). （24A0637）
