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Higher-Order Gradients: Hessian

Higher-Order Gradients: Hessian

Learn about higher-order gradients and the Hessian matrix.

Higher-order derivatives

Gradients and derivatives are also known as first-order derivatives. Algorithms like Newton’s method require computing higher-order derivatives, such as second-order derivatives. Given a multivariate function f(x1,x2,...,xm):RmRf(x_1, x_2, ..., x_m): \R^m \rightarrow \R, higher-order gradients/derivatives are represented as follows:

  • 2fxi2\frac{\partial^2 f}{\partial x_i^2} is known as the second partial derivative of ff ...