浙江大学学报（理学版）2026，Vol.53Issue(1)：78-87,10.DOI:10.3785/1008-9497.25013
一种多参数G3高精度的八次Hermite插值样条
A class of G3 high precision eighth-degree Hermite interpolation splines with multiple parameters
摘要
Abstract
To address the issues of high continuity and high precision in engineering calculations,this paper introduces an eighth-degree Hermite-type interpolation spline featuring high-order continuity,high precision,and multiple parameters.Initially,within the polynomial space,a novel approach for constructing Hermite-type basis functions with multiple parameters is presented by leveraging high-order continuity conditions and solving equation systems.Subsequently,the corresponding high-order interpolation spline is defined.Furthermore,a method for selecting parameters to achieve optimal interpolation is proposed.Lastly,the interpolation residual and the determination of the optimal interpolation function are discussed,and the effectiveness and high precision of the interpolation spline are validated through examples.Compared to existing piecewise Hermite-type interpolation splines with parameters,this eighth-degree Hermite interpolation spline automatically satisfies G3 continuity without any additional conditions,combining shape adjustability with high-order continuity,thereby exhibiting broader application prospects.关键词
G3连续性/高精度/八次Hermite样条/最优参数/最优插值函数Key words
G3 continous/high precision/eighth-degree Hermite spline/optimal parameter/optimal interpolation function分类
信息技术与安全科学引用本文复制引用
XIE Jin,YIN Hang..一种多参数G3高精度的八次Hermite插值样条[J].浙江大学学报（理学版）,2026,53(1):78-87,10.基金项目
国家自然科学基金项目(60973050). （60973050）
