Extrema detection of bivariate spline functions
type: Item
instance of: scholarly article
title: Extrema detection of bivariate spline functions
zbMATH Open document ID: 1152.65022
author: Hiroyuki Kano
author: H. Fujioka
author: Clyde Martin
published in: Applied Mathematics and Computation
publication date: 2008-06-17T00:00:00Z
review text: The problem of finding the extrema of a two-variable spline function \(x(s,t)\) of degree \(k\geq 3\), in a rectangle \(\mathcal{D}\subset \mathbb{R}^2\), is examined. In this respect, a method is developed which allows to detect the extrema of \(x(s,t)\) as well as of their derivatives. An exception is given by those extrema whose Hessian matrix is singular. The performance of the method is tested by considering an optimal smoothing spline which is designed by sampling the function \(f(s,t)=\sum_{i=1}^6 a_i \exp[-\kappa_i((s-p_i)^2+(t-q_i)^2)] \). Another example is the analysis of deformation of a jellyfish in motion. Some figures and tables are shown.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5289082
zbMATH Keywords: B-spline
zbMATH Keywords: spline approximation
zbMATH Keywords: bivariate spline
zbMATH Keywords: optimal smoothing spline
zbMATH Keywords: extrema
zbMATH Keywords: Hessian
zbMATH Keywords: resultant
reviewed by: J. Illán
MaRDI profile type: Publication
full work available at URL: j.amc.2007.10.054
OpenAlex ID: W2156072151
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DOI: 10.1016/J.AMC.2007.10.054
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description: scientific article; zbMATH DE number 5289082