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图学学报

• 专论：第12届中国计算机图形学大会 (CHINAGRAPH 2018 广州) • 上一篇    下一篇

插值区间型数据的鲁棒均匀 B-样条模型

  

  1. 1. 中南大学数学与统计学院，湖南 长沙 410083； 
    2. 伊利诺伊大学厄巴纳-香槟分校，伊利诺伊 厄巴纳 61801
  • 出版日期:2019-06-30 发布日期:2019-08-02
  • 基金资助:
    国家自然科学基金项目(11771453)；中南大学研究生创新项目(2016zzts013)

Robust Uniform B-Spline Models for Interpolating Interval Data

  1. 1. School of Mathematics and Statistics, Central South University, Changsha Hunan 410083, China;
    2. University of Illinois at Urbana-Champaign, Urbana IL 61801, United States
  • Online:2019-06-30 Published:2019-08-02

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摘要： 研究采用均匀 B-样条建立了插值区间型数据的鲁棒优化模型，与以传统多项式样 条为样条函数的鲁棒优化模型相比，存在表达式更为简单、计算过程更加容易等优势。该模型 是易解的有限凸优化问题，而传统多项式模型需要通过复杂变化，才能将带有无限个约束的凸 优化问题转化为有限优化问题。为增加模型的自由度，即插值曲线的可调性，首先讨论如何基 于给定的区间型数据扩建出建模过程中需要的全部特征多边形顶点的方法，之后具体采用工程 中经常使用的二次和三次均匀 B-样条，建立了适用于现有优化算法和软件的鲁棒优化模型，数 值实验部分证明了以上模型的易解性和有效性。

关键词: 区间型数据, 插值, B-样条, 鲁棒模型, 有限凸优化

Abstract: We adopted the uniform B-spline in building the robust models for interpolation problems of interval data. Compared with the robust models of the traditional polynomial spline, the B-spline models proposed in this paper have a number of advantages that enable a solution of an obvious finite convex optimization problem due to more concise formulations and a more simplified computing process. We put forward the method of creating the characteristic polygon vertices based on the given interval data for the purpose of increasing the freedom degree of models. The robust optimization models of the frequently used uniform quadratic and cubic B-spline are formulated in detail as finite convex optimization problems, which are applicable to the existing optimization algorithms and software. Some numerical examples are presented to show the feasibility and effectiveness of the proposed robust models.

Key words:  interval data, interpolation, B-spline, robust model, finite convex optimization