Symbolic Solutions to Division by Zero Problem via Gradient Neurodynamics

Abstract

Division by zero (DBZ) problem, or say, division singularity problem, has perplexed scientists and engineers in many fields for centuries. How to solve DBZ problem has actually been discussed for more than 1200 years. Despondingly, plenty of efforts failed to solve DBZ problem effectively, and it is still considered as a formidable conundrum. This paper introduce an extension of the division operation from a time-varying perspective. Most problems in science and engineering fields are time-varying, and thus the extension is reasonable and practical. Furthermore, by employing the neat gradient-based neurodynamics (or say, gradient neurodynamics) equation different times, a series of different “symbolic” solutions are proposed. Note that the proposed symbolic solutions have the ability to conquer DBZ problem. The symbolic solutions to DBZ problem may promote the development of more complete singularity-conquering applications.