Derivation of Augmented Arithmetic for Computing Gradient, Hessian and Jacobian through Forward Mode AD Using Dual Numbers

P.Senthil Vadivu, S. Ponnusamy


This paper presents a new approach to Automatic Differentiation (AD) for a scalar valued and twice continuously
differentiable function f : R^n - R. A new arithmetic is obtained based on the chain rule and using
augmented algebra of real numbers. The chain rule based differentiation arithmetic is used to find the Gradient
and Hessian. Jacobian is evaluated using Gradient arithmetic by computing Gradient for components and is arranged
in matrix form to give Jacobian value. The resulting derivative evaluation uses the operator overloading
concept which uses computer programs written in C++.

Full Text: PDF DOI: 10.5539/jmr.v1n1p35

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the '' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.