TY - JOUR
T1 - A method which finds the maxima and minima of a multivariable function applying affine arithmetic
AU - Miyajima, Shinya
AU - Kashiwagi, Masahide
PY - 2005/9/12
Y1 - 2005/9/12
N2 - A new method is proposed for finding all maxima and minima of a multivariable function f in a box X(0). In this method, the maxima and the minima are calculated by dividing X(0) into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.
AB - A new method is proposed for finding all maxima and minima of a multivariable function f in a box X(0). In this method, the maxima and the minima are calculated by dividing X(0) into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.
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M3 - Conference article
AN - SCOPUS:24144465149
VL - 3401
SP - 424
EP - 431
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
T2 - Third International Conference on Numerical Analysis and Its Applications, NAA 2004
Y2 - 29 June 2004 through 3 July 2004
ER -