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Extrema detection of bivariate spline functions |
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| Authors: | Hiroyuki Kano Hiroyuki Fujioka Clyde F Martin |
| Institution: | aDivision of Science, School of Science and Engineering, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-0394, Japan bDepartment of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA |
| Abstract: | 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. |
| Keywords: | B-spline Spline approximation Bivariate spline Extrema Hessian Resultant |
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