Extrema detection of bivariate spline functions

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• 作者：Hiroyuki Kano ; Hiroyuki Fujioka ; Clyde F. Martin
• 关键词：B-spline ; Spline approximation ; Bivariate spline ; Extrema ; Hessian ; Resultant
• 刊名：Applied Mathematics and Computation
• 出版年：2008
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 June 2008
• 卷：200
• 期：1
• 页码：58-69
• 文件大小：843 K

摘要

In this paper, we develop a systematic method for detecting the extrema of bivariate spline functions and of their derivatives. It is assumed that the splines are constituted by employing normalized, uniform B-splines as the basis functions, and the detection procedure fully utilizes the spline properties. All the extrema can be found except those with singular Hessian matrix. By numerical examples, we demonstrate the effectiveness of the method.