Tag Archives: third-order gradient

Third and higher order Taylor expansions in several variables

By psopasakis on November 5, 2016 | Leave a comment

In this post we show that it is possible to derive third and higer-order Taylor expansions for functions of several variables. Given that the gradient of a function $f:\mathbb{R}^n \to\mathbb{R}$ is vector-valued and its Hessian is matrix-valued, it is natural to guess that its third-order gradient will be tensor-valued. However, not only is the use of tensors not very convenient, but in this context it is also unnecessary. Continue reading →

Posted in: Optimisation | Tagged: Analysis, Calculus, directional derivative, directional Hessian, Hessian, Taylor expansion, third-order gradient

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Tag Archives: third-order gradient

Third and higher order Taylor expansions in several variables

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