Extremum of second-order directional derivatives |
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| Authors: | Gui-xia Lü Hao Wu Long-jun Shen |
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| Affiliation: | National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China. |
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| Abstract: | In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other. |
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| Keywords: | Finite point method second-order directional derivative extremum. |
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