• 先进计算 •

### 周期B样条基函数系数的并行算法

1. 1. 华侨大学 信息科学与工程学院，福建 泉州 362021
2. 华侨大学 机电及自动化学院，福建 泉州 362021
• 收稿日期:2010-12-15 修回日期:2011-02-07 发布日期:2011-07-01 出版日期:2011-07-01
• 通讯作者: 周凯汀
• 作者简介:周凯汀(1968-),女,辽宁大连人,副教授,硕士,主要研究方向：数值逼近、信号处理;郑力新(1967-),男,福建永春人,教授,博士,主要研究方向：信号处理、模式识别;林福泳(1959-),男,福建福州人,教授,博士,主要研究方向：工程计算、信号处理。
• 基金资助:

教育部科学技术研究重点项目;福建省高等学校新世纪优秀人才支持计划

### Parallel algorithm for computing coefficients of periodic B-spline basis functions

Kai-ting ZHOU1,Li-xin ZHENG1,Fu-yong LIN2

1. 1. College of Information Science and Engineering,Huaqiao University,Quanzhou Fujian 362021,China
2. College of Mechanical Engineering and Automation,Huaqiao University,Quanzhou Fujian 362021,China
• Received:2010-12-15 Revised:2011-02-07 Online:2011-07-01 Published:2011-07-01
• Contact: Kai-ting ZHOU

Abstract: In the existing methods of periodic B-spline interpolation, coefficients of B-spline basis functions are determined by iterative algorithms. To overcome the weakness of the existing methods, new parallel algorithm for computing coefficients of B-spline basis functions were established. First, this paper established orthogonal B-spline basis and derived parallel algorithm for coefficients of orthogonal B-spline basis functions; and then derived parallel algorithm for coefficients of B-spline basis functions by using the relation between coefficients of orthogonal B-spline basis functions and coefficients of B-spline basis functions; at last this paper derived explicit formulas for both coefficients of B-spline basis functions and value of interpolated point with the 2nd, the 3rd and the 4th order periodic interpolating B-spline functions. The presented method retains the simplicity of B-spline basis functions while realizing fast parallel algorithm for coefficients of B-spline basis functions.