Methods of determining the extreme points for trivariate functions

Weiren Zhao, Qian Wu, Chen He

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

There have been some researches in recent years, e.g. [2-5], on how to determine the extreme points of a smooth multivariate function, especially in the case where Hesse criterion is ineffective; however, most of the researches focus only on bivariate functions or lower-order stable points. In this essay we adopt Taylor series expansion of the function at the stable points, consider the positive definiteness of the corresponding homogeneous polynomial, raise the image criterion for determining the extreme points of a trivariate function, and finally extend the conclusions to higher-order situations. One fact is that this criterion is effective, and there's no need to consider the influence of the order of the stable points.

Original languageEnglish (US)
Title of host publication2011 International Conference on Multimedia Technology, ICMT 2011
Pages5930-5933
Number of pages4
DOIs
StatePublished - 2011
Event2nd International Conference on Multimedia Technology, ICMT 2011 - Hangzhou, China
Duration: Jul 26 2011Jul 28 2011

Publication series

Name2011 International Conference on Multimedia Technology, ICMT 2011

Conference

Conference2nd International Conference on Multimedia Technology, ICMT 2011
CountryChina
CityHangzhou
Period7/26/117/28/11

Keywords

  • Extreme point
  • Homogeneous polynomial
  • Smooth function
  • Stable point

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Human-Computer Interaction
  • Software

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  • Cite this

    Zhao, W., Wu, Q., & He, C. (2011). Methods of determining the extreme points for trivariate functions. In 2011 International Conference on Multimedia Technology, ICMT 2011 (pp. 5930-5933). [6001711] (2011 International Conference on Multimedia Technology, ICMT 2011). https://doi.org/10.1109/ICMT.2011.6001711