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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L J Shen, G X Lü, Z J Shen. A finite point method based on directional differences, SIAM J Numer Anal, 2009, 47(3): 2224–2242.
G X Lü, L J Shen, Z J Shen. Study on finite point method, Chinese J Comput Phys, 2008, 25(5): 505–524.
G X Lü, L J Shen, Z J Shen. Numerical methods for energy flux of temperature diffusion equation on unstructured grids, Int J Numer Meth Biomed Engng, 2010, 26(5): 646–665.
L Yin, G X Lü, L J Shen. Relations between 3D directional derivatives and expressions of typical differential operators, Appl Math J Chinese Univ Ser B, 2009, 24(2): 221–229.
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Supported by the National Natural Science Foundation of China (10871029, 11071025), the Foundation of CAEP (2010A0202010) and the Foundation of National Key Laboratory of Science and Technology on Computational Physics.
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Lü, Gx., Wu, H. & Shen, Lj. Extremum of second-order directional derivatives. Appl. Math. J. Chin. Univ. 26, 379–389 (2011). https://doi.org/10.1007/s11766-011-2535-7
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DOI: https://doi.org/10.1007/s11766-011-2535-7