Year: 2021
Type: preprint
Abstract: It has long been a goal to efficiently compute and use second order information on a function ($f$) to assist in numerical approximations. Here it is shown how, using only basic physics and a numerical approximation, such information can be accurately obtained at a cost of ${\cal O}(N)$ complexity, where $N$ is the dimensionality of the parameter space of $f$. In this paper, an algorithm ({\em VA-Flow}) is developed to exploit this second order information, and pseudocode is presented. It is applied to two classes of problems, that of inverse kinematics (IK) and gradient descent (GD). In the IK application, the algorithm is fast and robust, and is shown to lead to smooth behavior even near singularities. For GD the algorithm also works very well, provided the cost function is locally well-described by a polynomial.
Source: arXiv (Cornell University)
Author: Zimmer, Michael F.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3165583436