GitHub

( 3.5 ) Partial derivatives of composite functions : change of variables , ( 3.6) Partial differentiation of implicit functions

3.5 PARTIAL DIFFERENTIATION OF COMPOSITE FUNCTIONS: CHANGE OF VARIABLES In the study of heat equation, wave equation, and Laplace’s equation, it is very often required to transform the representing ...
IEEE

Symmetry of backpropagation and chain rule

Abstract: Gradient backpropagation, as a method of computing derivatives of composite functions, is commonly understood as a version of the chain rule. We show that this is not true, and both methods ...
Scientific Research Publishing

Derivative-Based Midpoint Quadrature Rule

A new family of numerical integration formula is presented, which uses the function evaluation at the midpoint of the interval and odd derivatives at the endpoints. Because the weights for the odd ...
GitHub

Interpolation-Based Composite Derivative-Free Optimization

This page contains source code for interpolation-based optimization methods for composite derivative-free optimization. Relevant references include: J. Larson and M. Menickelly. Structure-aware ...