TY - GEN
T1 - Methods of determining the extreme points for trivariate functions
AU - Zhao, Weiren
AU - Wu, Qian
AU - He, Chen
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Extreme point
KW - Homogeneous polynomial
KW - Smooth function
KW - Stable point
UR - http://www.scopus.com/inward/record.url?scp=80052937402&partnerID=8YFLogxK
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U2 - 10.1109/ICMT.2011.6001711
DO - 10.1109/ICMT.2011.6001711
M3 - Conference contribution
AN - SCOPUS:80052937402
SN - 9781612847740
T3 - 2011 International Conference on Multimedia Technology, ICMT 2011
SP - 5930
EP - 5933
BT - 2011 International Conference on Multimedia Technology, ICMT 2011
T2 - 2nd International Conference on Multimedia Technology, ICMT 2011
Y2 - 26 July 2011 through 28 July 2011
ER -